Journal de Mathematiques Pures et Appliquees最新文献

{"title":"Symplectic singularities arising from algebras of symmetric tensors","authors":"Baohua Fu ,&nbsp;Jie Liu","doi":"10.1016/j.matpur.2025.103794","DOIUrl":"10.1016/j.matpur.2025.103794","url":null,"abstract":"<div><div>The algebra of symmetric tensors <span><math><mi>S</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>≔</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>(</mo><mi>X</mi><mo>,</mo><msup><mrow><mi>S</mi></mrow><mrow><mo>•</mo></mrow></msup><msub><mrow><mi>T</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo></math></span> of a projective manifold <em>X</em> leads to a natural dominant affinization morphism<span><span><span><math><msub><mrow><mi>φ</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>:</mo><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>X</mi><mo>⟶</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>≔</mo><mi>Spec</mi><mspace></mspace><mi>S</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>.</mo></math></span></span></span> It is shown that <span><math><msub><mrow><mi>φ</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is birational if and only if <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is big. We prove that if <span><math><msub><mrow><mi>φ</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is birational, then <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is a symplectic variety endowed with the Schouten–Nijenhuis bracket if and only if <span><math><mi>P</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is of Fano type, which is the case for smooth projective toric varieties, smooth horospherical varieties with small boundary, and the quintic del Pezzo threefold. These give examples of a distinguished class of conical symplectic varieties, which we call symplectic orbifold cones.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"204 ","pages":"Article 103794"},"PeriodicalIF":2.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cremona equivalence and log Kodaira dimension","authors":"Massimiliano Mella","doi":"10.1016/j.matpur.2025.103793","DOIUrl":"10.1016/j.matpur.2025.103793","url":null,"abstract":"<div><div>Two projective varieties are said to be Cremona equivalent if there is a Cremona modification sending one onto the other. In the last decade, Cremona equivalence has been investigated widely, and we now have a complete theory for non-divisorial reduced schemes. The case of irreducible divisors is completely different, and not much is known besides the case of plane curves and a few classes of surfaces. In particular, for plane curves it is a classical result that an irreducible plane curve is Cremona equivalent to a line if and only if its log-Kodaira dimension is negative. This can be interpreted as the log version of Castelnuovo's rationality criterion for surfaces. One expects that a similar result for surfaces in projective space should not be true, as it is false, the generalization in higher dimensions of Castelnuovo's Rationality Theorem. In this paper, the first example of such behavior is provided, exhibiting a rational surface in the projective space with negative log-Kodaira dimension, which is not Cremona equivalent to a plane. This can be thought of as a sort of log Iskovkikh-Manin, Clemens-Griffith, Artin-Mumford example. Using this example, it is then possible to show that Cremona equivalence to a plane is neither open nor closed among log pairs with negative Kodaira dimension.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"204 ","pages":"Article 103793"},"PeriodicalIF":2.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145104686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Hamilton-Jacobi approach to road-field reaction-diffusion models","authors":"Christopher Henderson ,&nbsp;King-Yeung Lam","doi":"10.1016/j.matpur.2025.103798","DOIUrl":"10.1016/j.matpur.2025.103798","url":null,"abstract":"<div><div>We consider the road-field reaction-diffusion model introduced by Berestycki, Roquejoffre, and Rossi. By performing a “thin-front” limit, we are able to deduce a Hamilton-Jacobi equation with a suitable effective Hamiltonian on the road that governs the front location of the road-field model. Our main motivation is to apply the theory of strong (flux-limited) viscosity solutions in order to determine a control formulation interpretation of the front location. In view of the ecological meaning of the road-field model, this is natural as it casts the invasion problem as one of finding optimal paths that balance the positive growth rate in the field with the fast diffusion on the road.</div><div>Our main contribution is a nearly complete picture of the behavior on two-road conical domains. When the diffusivities on each road are the same, we show that the propagation speed in each direction in the cone can be computed via those associated with one-road half-space problem. When the diffusivities differ, we show that the speed along the faster road is unchanged, while the speed along the slower road can be enhanced. Along the way we provide a new proof of known results on the one-road half-space problem via our approach.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"205 ","pages":"Article 103798"},"PeriodicalIF":2.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145117576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Suppression of blow-up by local anisotropy of signal production in the Keller-Segel system","authors":"Youshan Tao ,&nbsp;Michael Winkler","doi":"10.1016/j.matpur.2025.103795","DOIUrl":"10.1016/j.matpur.2025.103795","url":null,"abstract":"<div><div>In a smoothly bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, <span><math><mi>n</mi><mo>≤</mo><mn>5</mn></math></span>, and with <span><math><mi>D</mi><mo>&gt;</mo><mn>0</mn></math></span> and <span><math><mi>d</mi><mo>&gt;</mo><mn>0</mn></math></span>, this manuscript considers the Neumann initial-boundary problem for the Keller-Segel type system<span><span><span><math><mrow><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>D</mi><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>u</mi><mi>∇</mi><mi>v</mi><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>d</mi><mi>Δ</mi><mi>v</mi><mo>+</mo><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>u</mi><mi>∇</mi><mi>v</mi><mo>)</mo><mo>−</mo><mi>v</mi><mo>+</mo><mi>u</mi><mo>,</mo></mtd></mtr></mtable></mrow><mspace></mspace><mo>(</mo><mo>⋆</mo><mo>)</mo></mrow></math></span></span></span> which arises in the modeling for chemotactic movement in the presence of certain anisotropic signal production mechanisms.</div><div>Unlike the classical Keller-Segel model whose solutions may blow up in finite time in high-dimensional domains, this problem is shown to admit a unique global bounded classical solution whenever the difference <span><math><mo>|</mo><mi>D</mi><mo>−</mo><mi>d</mi><mo>|</mo></math></span> is appropriately small. This markedly distinguishes (⋆) from classical Keller-Segel systems for which some solutions are known to blow up in finite time when <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"205 ","pages":"Article 103795"},"PeriodicalIF":2.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spectral analysis and phase transitions for long-range interactions in harmonic chains of oscillators","authors":"Simon Becker ,&nbsp;Angeliki Menegaki ,&nbsp;Jiming Yu","doi":"10.1016/j.matpur.2025.103796","DOIUrl":"10.1016/j.matpur.2025.103796","url":null,"abstract":"<div><div>We consider chains of <em>N</em> harmonic oscillators in two dimensions coupled to a Langevin heat reservoir at fixed temperature, a classical model for heat conduction introduced by Lebowitz, Lieb, and Rieder (1967). We extend our previous results (Becker and Menegaki, 2021) significantly by providing a full spectral description of the full Fokker-Planck operator, also allowing for the presence of a constant external magnetic field for charged oscillators. We then study oscillator chains with additional next-to-nearest-neighbor interactions and find that the spectral gap undergoes a phase transition if the next-to-nearest-neighbor interactions are sufficiently strong and may even cease to exist for oscillator chains of finite length.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"204 ","pages":"Article 103796"},"PeriodicalIF":2.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global regularity of integral 2-varifolds with square integrable mean curvature","authors":"Fabian Rupp ,&nbsp;Christian Scharrer","doi":"10.1016/j.matpur.2025.103797","DOIUrl":"10.1016/j.matpur.2025.103797","url":null,"abstract":"<div><div>We provide sharp sufficient criteria for an integral 2-varifold to be induced by a <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msup></math></span>-conformal immersion of a smooth surface. Our approach is based on a fine analysis of the Hausdorff density for 2-varifolds with critical integrability of the mean curvature and a recent local regularity result by Bi–Zhou. In codimension one, there are only three possible density values below 2, each of which can be attained with equality in the Li–Yau inequality for the Willmore functional by the unit sphere, the double bubble, and the triple bubble. We show that below an optimal threshold for the Willmore energy, a varifold induced by a current without boundary is in fact a curvature varifold with a uniform bound on its second fundamental form. Consequently, the minimization of the Willmore functional in the class of curvature varifolds with prescribed even Euler characteristic provides smooth solutions for the Willmore problem. In particular, the “ambient” varifold approach and the “parametric” approach are equivalent for minimizing the Willmore energy.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"204 ","pages":"Article 103797"},"PeriodicalIF":2.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Korn type inequalities for objective structures","authors":"Bernd Schmidt,&nbsp;Martin Steinbach","doi":"10.1016/j.matpur.2025.103779","DOIUrl":"10.1016/j.matpur.2025.103779","url":null,"abstract":"<div><div>We establish discrete Korn type inequalities for particle systems within the general class of objective structures that represents a far reaching generalization of crystal lattice structures. For space filling configurations whose symmetry group is a general space group we obtain a full discrete Korn inequality. For systems with non-trivial codimension our results provide an intrinsic rigidity estimate within the extended dimensions of the structure. As their continuum counterparts in elasticity theory, such estimates are at the core of energy estimates and, hence, a stability analysis for a wide class of atomistic particle systems.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"204 ","pages":"Article 103779"},"PeriodicalIF":2.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145104685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiple solutions to a semilinear elliptic equation with a sharp change of sign in the nonlinearity","authors":"Mónica Clapp ,&nbsp;Angela Pistoia ,&nbsp;Alberto Saldaña","doi":"10.1016/j.matpur.2025.103783","DOIUrl":"10.1016/j.matpur.2025.103783","url":null,"abstract":"<div><div>We consider a nonautonomous semilinear elliptic problem where the power-type nonlinearity is multiplied by a discontinuous coefficient that takes the value one inside a bounded open set Ω and minus one in its complement. In the slightly subcritical regime, we prove the existence of concentrating positive and nodal solutions. Moreover, depending on the geometry of Ω, we establish multiplicity of positive solutions. Finally, in the critical case, we show the existence of a blow-up positive solution when Ω has nontrivial topology. Our proofs rely on a Lyapunov-Schmidt reduction strategy which in these problems turns out to be remarkably simple. We take this opportunity to highlight certain aspects of the method that are often overlooked and present it in a more accessible and detailed manner for nonexperts.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"205 ","pages":"Article 103783"},"PeriodicalIF":2.3,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bubbling and quantitative stability for Alexandrov's Soap Bubble Theorem with L1-type deviations","authors":"Giorgio Poggesi","doi":"10.1016/j.matpur.2025.103784","DOIUrl":"10.1016/j.matpur.2025.103784","url":null,"abstract":"<div><div>The quantitative analysis of bubbling phenomena for almost constant mean curvature boundaries is an important question having significant applications in various fields including capillarity theory and the study of mean curvature flows. Such a quantitative analysis was initiated in Ciraolo and Maggi (2017) <span><span>[3]</span></span>, where the first quantitative result of proximity to a set of disjoint balls of equal radii was obtained in terms of a uniform deviation of the mean curvature from being constant. Weakening the measure of the deviation in such a result is a delicate issue that is crucial in view of the applications for mean curvature flows. Some progress in this direction was recently made in Julin and Niinikoski (2023) <span><span>[12]</span></span>, where <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span>-deviations are considered for domains in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. In the present paper we significantly weaken the measure of the deviation, obtaining a quantitative result of proximity to a set of disjoint balls of equal radii for the following deviation<span><span><span><math><munder><mo>∫</mo><mrow><mo>∂</mo><mi>Ω</mi></mrow></munder><msup><mrow><mo>(</mo><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>−</mo><mi>H</mi><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>,</mo><mspace></mspace><mtext> where </mtext><mrow><mo>{</mo><mtable><mtr><mtd><mi>H</mi><mtext> is the mean curvature of </mtext><mo>∂</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>:</mo><mo>=</mo><mfrac><mrow><mo>|</mo><mo>∂</mo><mi>Ω</mi><mo>|</mo></mrow><mrow><mi>N</mi><mo>|</mo><mi>Ω</mi><mo>|</mo></mrow></mfrac><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><mo>(</mo><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>−</mo><mi>H</mi><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup><mo>:</mo><mo>=</mo><mi>max</mi><mo>⁡</mo><mrow><mo>{</mo><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>−</mo><mi>H</mi><mo>,</mo><mn>0</mn><mo>}</mo></mrow><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> which is clearly even weaker than <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>−</mo><mi>H</mi><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mo>∂</mo><mi>Ω</mi><mo>)</mo></mrow></msub></math></span>.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"204 ","pages":"Article 103784"},"PeriodicalIF":2.3,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145009927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic and global analysis of principal eigenvalues for linear time-periodic parabolic systems","authors":"Shuang Liu","doi":"10.1016/j.matpur.2025.103781","DOIUrl":"10.1016/j.matpur.2025.103781","url":null,"abstract":"<div><div>The paper is concerned with the effects of the spatio-temporal heterogeneity on the principal eigenvalues of some linear time-periodic parabolic systems. Various asymptotic behaviors of the principal eigenvalue and its monotonicity, as a function of the diffusion rate and frequency, are derived. In particular, some singular behaviors of the principal eigenvalues are characterized when both the diffusion rate and frequency approach zero, with some scalar time-periodic Hamilton-Jacobi equation as the limiting equation. Furthermore, we completely classify the topological structures of the level sets for the principal eigenvalues in the plane of the diffusion rate and frequency. Our results not only generalize the findings in <span><span>[28]</span></span> for scalar periodic-parabolic operators, but also reveal more rich global information, for time-periodic parabolic systems, on the dependence of the principal eigenvalues upon the spatio-temporal heterogeneity.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"203 ","pages":"Article 103781"},"PeriodicalIF":2.3,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}