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An Example on s-H-Convexity in $$pmb {mathbb {C}^2}$$ 中的s- h -凸性的一个例子 $$pmb {mathbb {C}^2}$$
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2020-01-27 DOI: 10.1007/s12220-020-00359-5
Lars Simon, Berit Stensønes
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引用次数: 0
The Heat Asymptotics on Filtered Manifolds. 滤波流形上的热渐近。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2020-01-01 Epub Date: 2019-01-23 DOI: 10.1007/s12220-018-00137-4
Shantanu Dave, Stefan Haller
{"title":"The Heat Asymptotics on Filtered Manifolds.","authors":"Shantanu Dave, Stefan Haller","doi":"10.1007/s12220-018-00137-4","DOIUrl":"10.1007/s12220-018-00137-4","url":null,"abstract":"<p><p>The short-time heat kernel expansion of elliptic operators provides a link between local and global features of classical geometries. For many geometric structures related to (non-)involutive distributions, the natural differential operators tend to be Rockland, hence hypoelliptic. In this paper, we establish a universal heat kernel expansion for formally self-adjoint non-negative Rockland differential operators on general closed filtered manifolds. The main ingredient is the analysis of parametrices in a recently constructed calculus adapted to these geometric structures. The heat expansion implies that the new calculus, a more general version of the Heisenberg calculus, also has a non-commutative residue. Many of the well-known implications of the heat expansion such as, the structure of the complex powers, the heat trace asymptotics, the continuation of the zeta function, as well as Weyl's law for the eigenvalue asymptotics, can be adapted to this calculus. Other consequences include a McKean-Singer type formula for the index of Rockland differential operators. We illustrate some of these results by providing a more explicit description of Weyl's law for Rumin-Seshadri operators associated with curved BGG sequences over 5-manifolds equipped with a rank-two distribution of Cartan type.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"30 1","pages":"337-389"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6994647/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37647622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Interpolating Sesqui-Harmonic Maps Between Riemannian Manifolds. 黎曼流形间的倍谐插值映射。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2020-01-01 Epub Date: 2019-01-14 DOI: 10.1007/s12220-018-00130-x
Volker Branding
{"title":"On Interpolating Sesqui-Harmonic Maps Between Riemannian Manifolds.","authors":"Volker Branding","doi":"10.1007/s12220-018-00130-x","DOIUrl":"https://doi.org/10.1007/s12220-018-00130-x","url":null,"abstract":"<p><p>Motivated from the action functional for bosonic strings with extrinsic curvature term we introduce an action functional for maps between Riemannian manifolds that interpolates between the actions for harmonic and biharmonic maps. Critical points of this functional will be called interpolating sesqui-harmonic maps. In this article we initiate a rigorous mathematical treatment of this functional and study various basic aspects of its critical points.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"30 1","pages":"248-273"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-018-00130-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37647621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Analytical Properties for Degenerate Equations 退化方程的解析性质
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2020-01-01 DOI: 10.1007/978-3-030-34953-0_4
T. Colding, W. Minicozzi
{"title":"Analytical Properties for Degenerate Equations","authors":"T. Colding, W. Minicozzi","doi":"10.1007/978-3-030-34953-0_4","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_4","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"73 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85827990","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: 1
Applications of Min–Max Methods to Geometry 最小-最大方法在几何中的应用
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2020-01-01 DOI: 10.1007/978-3-030-53725-8_2
F. C. Marques, A. Neves
{"title":"Applications of Min–Max Methods to Geometry","authors":"F. C. Marques, A. Neves","doi":"10.1007/978-3-030-53725-8_2","DOIUrl":"https://doi.org/10.1007/978-3-030-53725-8_2","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"245 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73188941","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: 4
Pseudo-Hermitian Geometry in 3D 三维伪厄米几何
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2020-01-01 DOI: 10.1007/978-3-030-53725-8_4
Paul Yang
{"title":"Pseudo-Hermitian Geometry in 3D","authors":"Paul Yang","doi":"10.1007/978-3-030-53725-8_4","DOIUrl":"https://doi.org/10.1007/978-3-030-53725-8_4","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"111 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80685667","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
Ultradifferentiable CR Manifolds. 超可微CR流形。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2020-01-01 Epub Date: 2019-04-18 DOI: 10.1007/s12220-019-00191-6
Stefan Fürdös
{"title":"Ultradifferentiable CR Manifolds.","authors":"Stefan Fürdös","doi":"10.1007/s12220-019-00191-6","DOIUrl":"https://doi.org/10.1007/s12220-019-00191-6","url":null,"abstract":"<p><p>In this article, the notion of ultradifferentiable CR manifold is introduced and an ultradifferentiable regularity result for finitely nondegenerate CR mappings is proven. Here, ultradifferentiable means with respect to Denjoy-Carleman classes defined by weight sequences. Furthermore, the regularity of infinitesimal CR automorphisms on ultradifferentiable abstract CR manifolds is investigated.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"30 3","pages":"3064-3098"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-019-00191-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38118322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A Phragmén-Lindelöf Theorem via Proximate Orders, and the Propagation of Asymptotics. 一个近似阶的Phragmén-Lindelöf定理，以及渐近的传播。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2020-01-01 Epub Date: 2019-05-10 DOI: 10.1007/s12220-019-00203-5
Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl
{"title":"A Phragmén-Lindelöf Theorem via Proximate Orders, and the Propagation of Asymptotics.","authors":"Javier Jiménez-Garrido,&nbsp;Javier Sanz,&nbsp;Gerhard Schindl","doi":"10.1007/s12220-019-00203-5","DOIUrl":"https://doi.org/10.1007/s12220-019-00203-5","url":null,"abstract":"<p><p>We prove that, for asymptotically bounded holomorphic functions in a sector in <math><mrow><mi>C</mi> <mo>,</mo></mrow> </math> an asymptotic expansion in a single direction towards the vertex with constraints in terms of a logarithmically convex sequence admitting a nonzero proximate order entails asymptotic expansion in the whole sector with control in terms of the same sequence. This generalizes a result by Fruchard and Zhang for Gevrey asymptotic expansions, and the proof strongly rests on a suitably refined version of the classical Phragmén-Lindelöf theorem, here obtained for functions whose growth in a sector is specified by a nonzero proximate order in the sense of Lindelöf and Valiron.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"30 4","pages":"3458-3483"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-019-00203-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38553057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
$${mathbf {L}}^{{mathbf {p}}}$$-Sobolev Estimates for a Class of Integral Operators with Folding Canonical Relations $${mathbf {L}}^{{mathbf {p}}}$$一类具有可折叠正则关系的积分算子的-Sobolev估计
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2019-09-09 DOI: 10.1007/s12220-020-00388-0
M. Pramanik, A. Seeger
{"title":"$${mathbf {L}}^{{mathbf {p}}}$$-Sobolev Estimates for a Class of Integral Operators with Folding Canonical Relations","authors":"M. Pramanik, A. Seeger","doi":"10.1007/s12220-020-00388-0","DOIUrl":"https://doi.org/10.1007/s12220-020-00388-0","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-41"},"PeriodicalIF":1.1,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-020-00388-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47311598","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: 6
Fourier–Mukai Transforms, Euler–Green Currents, and K-Stability 傅里叶-穆凯变换，欧拉-格林电流和k -稳定性
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2019-04-30 DOI: 10.1007/978-3-030-34953-0_14
S. Paul, Kyriakos Sergiou
{"title":"Fourier–Mukai Transforms, Euler–Green Currents, and K-Stability","authors":"S. Paul, Kyriakos Sergiou","doi":"10.1007/978-3-030-34953-0_14","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_14","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"90 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88743174","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: 1
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