Bulletin des Sciences Mathematiques最新文献

{"title":"The Hausdorff distance and metrics on toric singularity types","authors":"A. Aitokhuehi ,&nbsp;B. Braiman ,&nbsp;D. Cutler ,&nbsp;T. Darvas ,&nbsp;R. Deaton ,&nbsp;P. Gupta ,&nbsp;J. Horsley ,&nbsp;V. Pidaparthy ,&nbsp;J. Tang","doi":"10.1016/j.bulsci.2025.103714","DOIUrl":"10.1016/j.bulsci.2025.103714","url":null,"abstract":"<div><div>Given a compact Kähler manifold <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span>, due to the work of Darvas–Di Nezza–Lu, the space of singularity types of <em>ω</em>-psh functions admits a natural pseudo-metric <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span> that is complete in the presence of positive mass. When restricted to model singularity types, this pseudo-metric is a bona fide metric.</div><div>In case of the projective space, there is a known one-to-one correspondence between toric model singularity types and convex bodies inside the unit simplex. Hence in this case it is natural to compare the <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span> metric to the classical Hausdorff metric. We provide precise Hölder bounds, showing that their induced topologies are the same.</div><div>More generally, we introduce a quasi-metric <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> on the space of compact convex sets inside an arbitrary convex body <em>G</em>, with <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>S</mi></mrow></msub><mo>=</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> in case <em>G</em> is the unit simplex. We prove optimal Hölder bounds comparing <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> with the Hausdorff metric. Our analysis shows that the Hölder exponents differ depending on the geometry of <em>G</em>, with the worst exponents in case <em>G</em> is a polytope, and the best in case <em>G</em> has <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> boundary.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103714"},"PeriodicalIF":0.9,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144904500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the similarity of operators restricted to an invariant subspace","authors":"Kui Ji ,&nbsp;Shanshan Ji ,&nbsp;Dinesh Kumar Keshari ,&nbsp;Jing Xu","doi":"10.1016/j.bulsci.2025.103712","DOIUrl":"10.1016/j.bulsci.2025.103712","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span> be the multiplication operator on the Bergman space and <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>I</mi></mrow></msub></math></span> denote the restriction of <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span> to an invariant subspace <em>I</em>. A question raised by K. Zhu in <span><span>[44]</span></span> is when two restriction operators <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>I</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>J</mi></mrow></msub></math></span> are similar. Influenced by this open question, this note considers a more general case. Specifically, the multiplication operator on the Bergman space is replaced by the adjoint of Cowen-Douglas operators, and a direct sum of the multiplication operator acting on certain analytic functional Hilbert spaces. Furthermore, we give some sufficient conditions for these questions involving complex geometric objects of Hermitian holomorphic vector bundles.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103712"},"PeriodicalIF":0.9,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lp-Lq estimates for transition semigroups associated to dissipative stochastic systems","authors":"Luciana Angiuli ,&nbsp;Davide A. Bignamini ,&nbsp;Simone Ferrari","doi":"10.1016/j.bulsci.2025.103713","DOIUrl":"10.1016/j.bulsci.2025.103713","url":null,"abstract":"<div><div>In a separable Hilbert space, we study supercontractivity and ultracontractivity properties for a transition semigroup associated with a stochastic partial differential equation. This is done in terms of exponential integrability of Lipschitz functions and some logarithmic Sobolev-type inequalities with respect to invariant measures. The abstract characterization results concerning the improvement of summability can be applied to transition semigroups associated to stochastic reaction-diffusion equations.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103713"},"PeriodicalIF":0.9,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Martingale and analytic dimensions coincide under Gaussian heat kernel bounds","authors":"Mathav Murugan","doi":"10.1016/j.bulsci.2025.103710","DOIUrl":"10.1016/j.bulsci.2025.103710","url":null,"abstract":"<div><div>Given a strongly local Dirichlet form on a metric measure space that satisfies Gaussian heat kernel bounds, we show that the martingale dimension of the associated diffusion process coincides with Cheeger's analytic dimension of the underlying metric measure space. More precisely, we show that the pointwise version of the martingale dimension introduced by Hino (called the pointwise index) almost everywhere equals the pointwise dimension of the measurable differentiable structure constructed by Cheeger. Using known properties of spaces that admit a measurable differentiable structure, we show that the martingale dimension is bounded from above by the Hausdorff dimension of the underlying metric space, thereby extending an earlier bound obtained by Hino for some self-similar sets.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103710"},"PeriodicalIF":0.9,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144885567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gradient estimates for Δbu + aup+1 = 0 on pseudo-Hermitian manifolds","authors":"Biqiang Zhao","doi":"10.1016/j.bulsci.2025.103709","DOIUrl":"10.1016/j.bulsci.2025.103709","url":null,"abstract":"<div><div>In this paper, we derive the gradient estimates for the positive solutions of the equation <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>b</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>a</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>=</mo><mn>0</mn></math></span> on complete noncompact pseudo-Hermitian manifolds, where <span><math><mi>a</mi><mo>&gt;</mo><mn>0</mn></math></span> and <span><math><mi>p</mi><mo>≤</mo><mn>0</mn></math></span> or <span><math><mi>a</mi><mo>&lt;</mo><mn>0</mn></math></span> and <span><math><mi>p</mi><mo>&gt;</mo><mn>0</mn></math></span> are two constants. As an application, we will obtain a Liouville-type theorem when the manifolds are Sasakian-type with nonnegative pseudo-Hermitian Ricci curvature.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103709"},"PeriodicalIF":0.9,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of the Kirchhoff-type plate equation with nonlinear damping","authors":"Ling Xu,&nbsp;Tingting Liu,&nbsp;Xue Bai","doi":"10.1016/j.bulsci.2025.103706","DOIUrl":"10.1016/j.bulsci.2025.103706","url":null,"abstract":"<div><div>The current paper is devoted to global well-posedness and the existence of global attractors for a Kirchhoff-type plate equation with nonlinear damping. To demonstrate the existence of global attractors, we mainly use the energy method in a priori estimations, and then verify the asymptotic compactness of the semigroup by the method of contraction functions.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103706"},"PeriodicalIF":0.9,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to “Stability of linear operators in locally convex cones” [Bull. Sci. Math. 191 (2024) 103380]","authors":"Iz-iddine EL-Fassi ,&nbsp;Abbas Najati","doi":"10.1016/j.bulsci.2025.103703","DOIUrl":"10.1016/j.bulsci.2025.103703","url":null,"abstract":"","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103703"},"PeriodicalIF":1.3,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Braid groups and mapping class groups for 2-orbifolds","authors":"Jonas Flechsig","doi":"10.1016/j.bulsci.2025.103705","DOIUrl":"10.1016/j.bulsci.2025.103705","url":null,"abstract":"<div><div>The main result of this article is that pure orbifold braid groups fit into an exact sequence<span><span><span><math><mn>1</mn><mo>→</mo><mi>K</mi><mo>→</mo><msubsup><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>o</mi><mi>r</mi><mi>b</mi></mrow></msubsup><mo>(</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mi>Γ</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>+</mo><mi>L</mi><mo>)</mo><mo>)</mo><mover><mrow><mo>→</mo></mrow><mrow><msub><mrow><mi>ι</mi></mrow><mrow><msub><mrow><mi>PZ</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub></mrow></mover><msub><mrow><mi>PZ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mi>Γ</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo><mo>)</mo><mover><mrow><mo>→</mo></mrow><mrow><msub><mrow><mi>π</mi></mrow><mrow><msub><mrow><mi>PZ</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub></mrow></mover><msub><mrow><mi>PZ</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mi>Γ</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo><mo>)</mo><mo>→</mo><mn>1</mn><mo>.</mo></math></span></span></span> In particular, we observe that the kernel <em>K</em> of <span><math><msub><mrow><mi>ι</mi></mrow><mrow><msub><mrow><mi>PZ</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub></math></span> is non-trivial. This corrects Theorem 2.14 in <span><span>[14]</span></span>. Moreover, we use the presentation of the pure orbifold mapping class group <span><math><msubsup><mrow><mi>PMap</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>id</mi><mo>,</mo><mi>o</mi><mi>r</mi><mi>b</mi></mrow></msubsup><mspace></mspace><mrow><mo>(</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mi>Γ</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo><mo>)</mo></mrow></math></span> from <span><span>[9]</span></span> to determine <em>K</em>. Comparing these orbifold mapping class groups with the orbifold braid groups, reveals a surprising behavior: in contrast to the classical case, the orbifold braid group is a proper quotient of the orbifold mapping class group. This yields a presentation of the pure orbifold braid group which allows us to read off the kernel <em>K</em>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103705"},"PeriodicalIF":0.9,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Boundedness of sublinear operators on grand central Orlicz-Morrey spaces","authors":"Mehvish Sultan ,&nbsp;Babar Sultan","doi":"10.1016/j.bulsci.2025.103704","DOIUrl":"10.1016/j.bulsci.2025.103704","url":null,"abstract":"<div><div>In this work, our first objective is to define the ideas of the grand <em>λ</em>-central Orlicz-BMO spaces and the grand central Orlicz-Morrey spaces. Next we prove the boundedness of sublinear operator and fractional integral operator on grand central Orlicz-Morrey spaces under some proper assumptions.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103704"},"PeriodicalIF":1.3,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence and uniqueness for a new class of fractional Laplacian equations on compact Riemannian manifold","authors":"Jinxia Cen ,&nbsp;J. Vanterler da C. Sousa ,&nbsp;Leandro S. Tavares","doi":"10.1016/j.bulsci.2025.103702","DOIUrl":"10.1016/j.bulsci.2025.103702","url":null,"abstract":"<div><div>In this article, we are first interested in presenting some technical results (lemmas) in the Riemannian manifold. In this sense, we investigate the existence and uniqueness of non-trivial solutions for a new class of Laplacian on compact Riemannian manifolds.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103702"},"PeriodicalIF":1.3,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144696602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}