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Journal fur die Reine und Angewandte Mathematik最新文献

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Frontmatter
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-06-01 DOI: 10.1515/crelle-2021-frontmatter775
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引用次数: 0
Representation by sums of unlike powers 用不同幂的和表示
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-05-27 DOI: 10.1515/crelle-2021-0048
Jianya Liu, Lilu Zhao
{"title":"Representation by sums of unlike powers","authors":"Jianya Liu, Lilu Zhao","doi":"10.1515/crelle-2021-0048","DOIUrl":"https://doi.org/10.1515/crelle-2021-0048","url":null,"abstract":"Abstract It is proved that all sufficiently large integers n can be represented as n=x12+x23+⋯+x1314,n=x_{1}^{2}+x_{2}^{3}+cdots+x_{13}^{14}, where x1,…,x13{x_{1},ldots,x_{13}} are positive integers. This improves upon the current record with fourteen variables in place of thirteen.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86665276","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}
引用次数: 5
Capillary surfaces: Stability, index and curvature estimates 毛细管表面:稳定性，指数和曲率估计
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-05-26 DOI: 10.1515/crelle-2023-0050
Hansol Hong, Artur B. Saturnino
{"title":"Capillary surfaces: Stability, index and curvature estimates","authors":"Hansol Hong, Artur B. Saturnino","doi":"10.1515/crelle-2023-0050","DOIUrl":"https://doi.org/10.1515/crelle-2023-0050","url":null,"abstract":"Abstract In this paper, we investigate the connection between the index and the geometry and topology of capillary surfaces. We prove an index estimate for compact capillary surfaces immersed in general 3-manifolds with boundary. We also study noncompact capillary surfaces with finite index and show that, under suitable curvature assumptions, such surface is conformally equivalent to a compact Riemann surface with boundary, punctured at finitely many points. We then prove that a weakly stable capillary surface immersed in a half-space of R 3 mathbb{R}^{3} which is minimal or has a contact angle less than or equal to π / 2 pi/2 must be a half-plane. Using this uniqueness result, we obtain curvature estimates for strongly stable capillary surfaces immersed in a 3-manifold with bounded geometry.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90234181","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}
引用次数: 4
Rigidity of four-dimensional gradient shrinking Ricci solitons 四维梯度收缩里奇孤子的刚性
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-05-22 DOI: 10.1515/crelle-2023-0042
Xu Cheng, Detang Zhou
{"title":"Rigidity of four-dimensional gradient shrinking Ricci solitons","authors":"Xu Cheng, Detang Zhou","doi":"10.1515/crelle-2023-0042","DOIUrl":"https://doi.org/10.1515/crelle-2023-0042","url":null,"abstract":"Abstract Let ( M , g , f ) {{(M,g,f)}} be a four-dimensional complete noncompact gradient shrinking Ricci soliton with the equation Ric + ∇ 2 ⁡ f = λ ⁢ g {{mathrm{Ric}+nabla^{2}f=lambda g}} , where λ {{lambda}} is a positive real number. We prove that if M {{M}} has constant scalar curvature S = 2 ⁢ λ {{S=2lambda}} , it must be a quotient of 𝕊 2 × ℝ 2 {{mathbb{S}^{2}timesmathbb{R}^{2}}} . Together with the known results, this implies that a four-dimensional complete gradient shrinking Ricci soliton has constant scalar curvature if and only if it is rigid, that is, it is either Einstein, or a finite quotient of Gaussian shrinking soliton ℝ 4 {{mathbb{R}^{4}}} , 𝕊 2 × ℝ 2 {{mathbb{S}^{2}timesmathbb{R}^{2}}} or 𝕊 3 × ℝ {{mathbb{S}^{3}timesmathbb{R}}} .","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82185703","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}
引用次数: 5
Eisenstein series and the top degree cohomology of arithmetic subgroups of SLn/ℚ SLn/ π算术子群的爱森斯坦级数与上次上同调
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-05-18 DOI: 10.1515/crelle-2021-0022
J. Schwermer
{"title":"Eisenstein series and the top degree cohomology of arithmetic subgroups of SLn/ℚ","authors":"J. Schwermer","doi":"10.1515/crelle-2021-0022","DOIUrl":"https://doi.org/10.1515/crelle-2021-0022","url":null,"abstract":"Abstract The cohomology H*⁢(Γ,E){H^{*}(Gamma,E)} of a torsion-free arithmetic subgroup Γ of the special linear ℚ{mathbb{Q}}-group 𝖦=SLn{mathsf{G}={mathrm{SL}}_{n}} may be interpreted in terms of the automorphic spectrum of Γ. Within this framework, there is a decomposition of the cohomology into the cuspidal cohomology and the Eisenstein cohomology. The latter space is decomposed according to the classes {𝖯}{{mathsf{P}}} of associate proper parabolic ℚ{mathbb{Q}}-subgroups of 𝖦{mathsf{G}}. Each summand H{P}*⁢(Γ,E){H^{*}_{mathrm{{P}}}(Gamma,E)} is built up by Eisenstein series (or residues of such) attached to cuspidal automorphic forms on the Levi components of elements in {𝖯}{{mathsf{P}}}. The cohomology H*⁢(Γ,E){H^{*}(Gamma,E)} vanishes above the degree given by the cohomological dimension cd⁢(Γ)=12⁢n⁢(n-1){mathrm{cd}(Gamma)=frac{1}{2}n(n-1)}. We are concerned with the internal structure of the cohomology in this top degree. On the one hand, we explicitly describe the associate classes {𝖯}{{mathsf{P}}} for which the corresponding summand H{𝖯}cd⁢(Γ)⁢(Γ,E){H^{mathrm{cd}(Gamma)}_{mathrm{{mathsf{P}}}}(Gamma,E)} vanishes. On the other hand, in the remaining cases of associate classes we construct various families of non-vanishing Eisenstein cohomology classes which span H{𝖰}cd⁢(Γ)⁢(Γ,ℂ){H^{mathrm{cd}(Gamma)}_{mathrm{{mathsf{Q}}}}(Gamma,mathbb{C})}. Finally, in the case of a principal congruence subgroup Γ⁢(q){Gamma(q)}, q=pν>5{q=p^{nu}>5}, p≥3{pgeq 3} a prime, we give lower bounds for the size of these spaces. In addition, for certain associate classes {𝖰}{{mathsf{Q}}}, there is a precise formula for their dimension.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91173569","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}
引用次数: 2
Modular symbols for Teichmüller curves teichm<e:1>曲线的模符号
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-05-12 DOI: 10.1515/crelle-2021-0019
C. McMullen
{"title":"Modular symbols for Teichmüller curves","authors":"C. McMullen","doi":"10.1515/crelle-2021-0019","DOIUrl":"https://doi.org/10.1515/crelle-2021-0019","url":null,"abstract":"Abstract This paper introduces a space of nonabelian modular symbols 𝒮⁢(V){{mathcal{S}}(V)} attached to any hyperbolic Riemann surface V, and applies it to obtain new results on polygonal billiards and holomorphic 1-forms. In particular, it shows the scarring behavior of periodic trajectories for billiards in a regular polygon is governed by a countable set of measures homeomorphic to ωω+1{omega^{omega}+1}.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82267404","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}
引用次数: 7
Geometric arcs and fundamental groups of rigid spaces 几何弧和刚性空间的基本群
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-05-11 DOI: 10.1515/crelle-2023-0013
Piotr Achinger, Marcin Lara, Alex Youcis
{"title":"Geometric arcs and fundamental groups of rigid spaces","authors":"Piotr Achinger, Marcin Lara, Alex Youcis","doi":"10.1515/crelle-2023-0013","DOIUrl":"https://doi.org/10.1515/crelle-2023-0013","url":null,"abstract":"Abstract We develop the notion of a geometric covering of a rigid space 𝑋, which yields a larger class of covering spaces than that studied previously by de Jong. Geometric coverings are closed under disjoint unions and are étale local on 𝑋. If 𝑋 is connected, its geometric coverings form a tame infinite Galois category and hence are classified by a topological group. The definition is based on the property of lifting of “geometric arcs” and is meant to be an analogue of the notion developed for schemes by Bhatt and Scholze.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76467722","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}
引用次数: 3
Conformal metrics with prescribed scalar and mean curvature 具有规定标量和平均曲率的共形度量
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-05-10 DOI: 10.1515/crelle-2022-0026
Sergio Cruz-Blázquez, A. Malchiodi, D. Ruiz
{"title":"Conformal metrics with prescribed scalar and mean curvature","authors":"Sergio Cruz-Blázquez, A. Malchiodi, D. Ruiz","doi":"10.1515/crelle-2022-0026","DOIUrl":"https://doi.org/10.1515/crelle-2022-0026","url":null,"abstract":"Abstract We consider the case with boundary of the classical Kazdan–Warner problem in dimension greater or equal than three, i.e. the prescription of scalar and boundary mean curvatures via conformal deformations of the metric. We deal in particular with negative scalar curvature and boundary mean curvature of arbitrary sign, which to our knowledge has not been treated in the literature. We employ a variational approach to prove new existence results, especially in three dimensions. One of the principal issues for this problem is to obtain compactness properties, due to the fact that bubbling may occur with profiles of hyperbolic balls or horospheres, and hence one may lose either pointwise estimates on the conformal factor or the total conformal volume. We can sometimes prevent them using integral estimates, Pohozaev identities and domain-variations of different types.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85839319","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}
引用次数: 6
On superintegral Kleinian sphere packings, bugs, and arithmetic groups 关于超积分Kleinian球填充、缺陷和算术群
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-04-28 DOI: 10.1515/crelle-2023-0004
M. Kapovich, Alex Kontorovich
{"title":"On superintegral Kleinian sphere packings, bugs, and arithmetic groups","authors":"M. Kapovich, Alex Kontorovich","doi":"10.1515/crelle-2023-0004","DOIUrl":"https://doi.org/10.1515/crelle-2023-0004","url":null,"abstract":"Abstract We develop the notion of a Kleinian Sphere Packing, a generalization of “crystallographic” (Apollonian-like) sphere packings defined in [A. Kontorovich and K. Nakamura, Geometry and arithmetic of crystallographic sphere packings, Proc. Natl. Acad. Sci. USA 116 2019, 2, 436–441]. Unlike crystallographic packings, Kleinian packings exist in all dimensions, as do “superintegral” such. We extend the Arithmeticity Theorem to Kleinian packings, that is, the superintegral ones come from ℚ {{mathbb{Q}}} -arithmetic lattices of simplest type. The same holds for more general objects we call Kleinian Bugs, in which the spheres need not be disjoint but can meet with dihedral angles π m {frac{pi}{m}} for finitely many m. We settle two questions from Kontorovich and Nakamura (2019): (i) that the Arithmeticity Theorem is in general false over number fields, and (ii) that integral packings only arise from non-uniform lattices.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90627683","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}
引用次数: 12
Gruson–Serganova character formulas and the Duflo–Serganova cohomology functor Gruson-Serganova特征公式和dufl - serganova上同调函子
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-04-26 DOI: 10.1515/crelle-2022-0080
M. Gorelik, T. Heidersdorf
{"title":"Gruson–Serganova character formulas and the Duflo–Serganova cohomology functor","authors":"M. Gorelik, T. Heidersdorf","doi":"10.1515/crelle-2022-0080","DOIUrl":"https://doi.org/10.1515/crelle-2022-0080","url":null,"abstract":"Abstract We establish an explicit formula for the character of an irreducible finite-dimensional representation of g ⁢ l ⁢ ( m | n ) mathfrak{gl}(m|n) . The formula is a finite sum with integer coefficients in terms of a basis E μ mathcal{E}_{mu} (Euler characters) of the character ring. We prove a simple formula for the behavior of the “superversion” of E μ mathcal{E}_{mu} in the g ⁢ l ⁢ ( m | n ) mathfrak{gl}(m|n) and o ⁢ s ⁢ p ⁢ ( m | 2 ⁢ n ) mathfrak{osp}(m|2n) -case under the map ds mathrm{ds} on the supercharacter ring induced by the Duflo–Serganova cohomology functor DS mathrm{DS} . As an application, we get combinatorial formulas for superdimensions, dimensions and g 0 mathfrak{g}_{0} -decompositions for g ⁢ l ⁢ ( m | n ) mathfrak{gl}(m|n) and o ⁢ s ⁢ p ⁢ ( m | 2 ⁢ n ) mathfrak{osp}(m|2n) .","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78142415","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}
引用次数: 3
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