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Mathematische Annalen最新文献

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Resolvent estimates for the Stokes operator in bounded and exterior $$C^1$$ domains 斯托克斯算子在有界和外部 $$C^1$$ 域中的残差估计值
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-03 DOI: 10.1007/s00208-024-02956-z
Jun Geng, Zhongwei Shen
{"title":"Resolvent estimates for the Stokes operator in bounded and exterior $$C^1$$ domains","authors":"Jun Geng, Zhongwei Shen","doi":"10.1007/s00208-024-02956-z","DOIUrl":"https://doi.org/10.1007/s00208-024-02956-z","url":null,"abstract":"<p>We establish resolvent estimates in <span>(L^q)</span> spaces for the Stokes operator in a bounded <span>(C^1)</span> domain <span>(Omega )</span> in <span>(mathbb {R}^{d})</span>. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in <span>(L^q(Omega ; mathbb {C}^d))</span> for any <span>(1&lt; q&lt; infty )</span> and <span>(dge 2)</span>. The case of an exterior <span>(C^1)</span> domain is also studied.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"222 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The isoperimetric problem in the Riemannian manifold admitting a non-trivial conformal vector field 容纳非三维共形向量场的黎曼流形中的等周问题
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-03 DOI: 10.1007/s00208-024-02954-1
Jiayu Li, Shujing Pan
{"title":"The isoperimetric problem in the Riemannian manifold admitting a non-trivial conformal vector field","authors":"Jiayu Li, Shujing Pan","doi":"10.1007/s00208-024-02954-1","DOIUrl":"https://doi.org/10.1007/s00208-024-02954-1","url":null,"abstract":"<p>In this article, we will study the isoperimetric problem by introducing a mean curvature type flow in the Riemannian manifold endowed with a non-trivial conformal vector field. This flow preserves the volume of the bounded domain enclosed by a star-shaped hypersurface and decreases the area of hypersurface under certain conditions. We will prove the long time existence and convergence of the flow. As a result, the isoperimetric inequality for such a domain is established. Especially, we solve the isoperimetric problem for the star-shaped hypersurfaces in the Riemannian manifold endowed with a closed, non-trivial conformal vector field, a wide class of warped product spaces studied by Guan, Li and Wang is included.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"75 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The regularity of difference divisors 差分除法的规律性
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-30 DOI: 10.1007/s00208-024-02950-5
Baiqing Zhu
{"title":"The regularity of difference divisors","authors":"Baiqing Zhu","doi":"10.1007/s00208-024-02950-5","DOIUrl":"https://doi.org/10.1007/s00208-024-02950-5","url":null,"abstract":"<p>For a prime number <span>(p&gt;2)</span> and a finite extension <span>(F/mathbb {Q}_p)</span>, we explain the construction of the difference divisors on the unitary Rapoport–Zink spaces of hyperspecial level over <span>(mathcal {O}_{breve{F}})</span>, and the GSpin Rapoport–Zink spaces of hyperspecial level over <span>(breve{mathbb {Z}}_{p})</span> associated to a minuscule cocharacter <span>(mu )</span> and a basic element <i>b</i>. We prove the regularity of the difference divisors, find the formally smooth locus of both the special cycles and the difference divisors, by a purely deformation-theoretic approach.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"108 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Newton polygons of sums on curves I: local-to-global theorems 曲线上和的牛顿多边形 I：局部到全局定理
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-29 DOI: 10.1007/s00208-024-02949-y
Joe Kramer-Miller, James Upton
{"title":"Newton polygons of sums on curves I: local-to-global theorems","authors":"Joe Kramer-Miller, James Upton","doi":"10.1007/s00208-024-02949-y","DOIUrl":"https://doi.org/10.1007/s00208-024-02949-y","url":null,"abstract":"<p>The purpose of this article is to study Newton polygons of certain abelian <i>L</i>-functions on curves. Let <i>X</i> be a smooth affine curve over a finite field <span>(mathbb {F}_q)</span> and let <span>(rho :pi _1(X) rightarrow mathbb {C}_p^times )</span> be a finite character of order <span>(p^n)</span>. By previous work of the first author, the Newton polygon <span>({{,mathrm{text {NP}},}}(rho ))</span> lies above a ‘Hodge polygon’ <span>({{,mathrm{text {HP}},}}(rho ))</span> defined using ramification invariants of <span>(rho )</span>. In this article we study the contact between these two polygons. We prove that <span>({{,mathrm{text {NP}},}}(rho ))</span> and <span>({{,mathrm{text {HP}},}}(rho ))</span> share a vertex if and only if a corresponding vertex is shared between the Newton and Hodge polygons of ‘local’ <i>L</i>-functions associated to each ramified point of <span>(rho )</span>. As a consequence, we determine a necessary and sufficient condition for the coincidence of <span>({{,mathrm{text {NP}},}}(rho ))</span> and <span>({{,mathrm{text {HP}},}}(rho ))</span>.\u0000</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"29 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Compact Kähler three-folds with nef anti-canonical bundle 具有 nef 反典型束的紧凑凯勒三折叠
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-28 DOI: 10.1007/s00208-024-02934-5
Shin-ichi Matsumura, Xiaojun Wu
{"title":"Compact Kähler three-folds with nef anti-canonical bundle","authors":"Shin-ichi Matsumura, Xiaojun Wu","doi":"10.1007/s00208-024-02934-5","DOIUrl":"https://doi.org/10.1007/s00208-024-02934-5","url":null,"abstract":"<p>In this paper, we prove that a non-projective compact Kähler three-fold with nef anti-canonical bundle is, up to a finite étale cover, one of the following: a manifold with vanishing first Chern class; the product of a K3 surface and the projective line; or a projective space bundle over a two-dimensional torus. This result extends Cao–Höring’s structure theorem for projective manifolds to compact Kähler manifolds in dimension 3. For the proof, we investigate the Minimal Model Program for compact Kähler three-folds with nef anti-canonical bundles by using the positivity of direct image sheaves, <span>(mathbb {Q})</span>-conic bundles, and orbifold vector bundles.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"39 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Regularity results for quasiminima of a class of double phase problems 一类双相问题准极限的正则性结果
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-23 DOI: 10.1007/s00208-024-02947-0
Antonella Nastasi, Cintia Pacchiano Camacho
{"title":"Regularity results for quasiminima of a class of double phase problems","authors":"Antonella Nastasi, Cintia Pacchiano Camacho","doi":"10.1007/s00208-024-02947-0","DOIUrl":"https://doi.org/10.1007/s00208-024-02947-0","url":null,"abstract":"<p>We prove boundedness, Hölder continuity, Harnack inequality results for local quasiminima to elliptic double phase problems of <i>p</i>-Laplace type in the general context of metric measure spaces. The proofs follow a variational approach and they are based on the De Giorgi method, a careful phase analysis and estimates in the intrinsic geometries.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"18 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Families of automorphisms on abelian varieties 无常变体上的自形族
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-23 DOI: 10.1007/s00208-024-02943-4
Charles Favre, Alexandra Kuznetsova
{"title":"Families of automorphisms on abelian varieties","authors":"Charles Favre, Alexandra Kuznetsova","doi":"10.1007/s00208-024-02943-4","DOIUrl":"https://doi.org/10.1007/s00208-024-02943-4","url":null,"abstract":"<p>We consider some algebraic aspects of the dynamics of an automorphism on a family of polarized abelian varieties parameterized by the complex unit disk. When the action on the cohomology of the generic fiber has no cyclotomic factor, we prove that such a map can be made regular only if the family of abelian varieties does not degenerate. As a contrast, we show that families of translations are always regularizable. We further describe the closure of the orbits of such maps, inspired by results of Cantat and Amerik–Verbitsky.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"2 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Caloric functions and boundary regularity for the fractional Laplacian in Lipschitz open sets 利普齐兹开集中分数拉普拉奇的热量函数和边界正则性
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-22 DOI: 10.1007/s00208-024-02931-8
Gavin Armstrong, Krzysztof Bogdan, Artur Rutkowski
{"title":"Caloric functions and boundary regularity for the fractional Laplacian in Lipschitz open sets","authors":"Gavin Armstrong, Krzysztof Bogdan, Artur Rutkowski","doi":"10.1007/s00208-024-02931-8","DOIUrl":"https://doi.org/10.1007/s00208-024-02931-8","url":null,"abstract":"<p>We give Martin representation of nonnegative functions caloric with respect to the fractional Laplacian in Lipschitz open sets. The caloric functions are defined in terms of the mean value property for the space-time isotropic <span>(alpha )</span>-stable Lévy process. To derive the representation, we first establish the existence of the parabolic Martin kernel. This involves proving new boundary regularity results for both the fractional heat equation and the fractional Poisson equation with Dirichlet exterior conditions. Specifically, we demonstrate that the ratio of the solution and the Green function is Hölder continuous up to the boundary.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"29 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Filling volume minimality and boundary rigidity of metrics close to a negatively curved symmetric metric 接近负弯对称度量的填充体积最小性和边界刚度
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-21 DOI: 10.1007/s00208-024-02941-6
Yuping Ruan
{"title":"Filling volume minimality and boundary rigidity of metrics close to a negatively curved symmetric metric","authors":"Yuping Ruan","doi":"10.1007/s00208-024-02941-6","DOIUrl":"https://doi.org/10.1007/s00208-024-02941-6","url":null,"abstract":"<p>This paper generalizes D. Burago and S. Ivanov’s work (Duke Math J 162:1205–1248, 2013) on filling volume minimality and boundary rigidity of almost real hyperbolic metrics. We show that regions with metrics close to a negatively curved symmetric metric are strict minimal fillings and hence boundary rigid. This includes perturbations of complex, quaternionic and Cayley hyperbolic metrics.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"26 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dirichlet spaces over chord-arc domains 弦弧域上的德里赫特空间
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-07-20 DOI: 10.1007/s00208-024-02946-1
Huaying Wei, Michel Zinsmeister
{"title":"Dirichlet spaces over chord-arc domains","authors":"Huaying Wei, Michel Zinsmeister","doi":"10.1007/s00208-024-02946-1","DOIUrl":"https://doi.org/10.1007/s00208-024-02946-1","url":null,"abstract":"<p>If <i>U</i> is a <span>(C^{infty })</span> function with compact support in the plane, we let <i>u</i> be its restriction to the unit circle <span>({mathbb {S}})</span>, and denote by <span>(U_i,,U_e)</span> the harmonic extensions of <i>u</i> respectively in the interior and the exterior of <span>({mathbb {S}})</span> on the Riemann sphere. About a hundred years ago, Douglas [9] has shown that </p><span>$$begin{aligned} iint _{{mathbb {D}}}|nabla U_i|^2(z)dxdy&amp;= iint _{bar{{mathbb {C}}}backslash bar{{mathbb {D}}}}|nabla U_e|^2(z)dxdy&amp;= frac{1}{2pi }iint _{{mathbb {S}}times {mathbb {S}}} left| frac{u(z_1)-u(z_2)}{z_1-z_2}right| ^2|dz_1||dz_2|, end{aligned}$$</span><p>thus giving three ways to express the Dirichlet norm of <i>u</i>. On a rectifiable Jordan curve <span>(Gamma )</span> we have obvious analogues of these three expressions, which will of course not be equal in general. The main goal of this paper is to show that these 3 (semi-)norms are equivalent if and only if <span>(Gamma )</span> is a chord-arc curve.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"10 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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