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Bakry-Émery Ricci Curvature Bounds for Doubly Warped Products of Weighted Spaces. 加权空间双翘曲积的Bakry-Émery Ricci曲率界。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2022-01-01 Epub Date: 2022-01-12 DOI: 10.1007/s12220-021-00745-7
Zohreh Fathi, Sajjad Lakzian
{"title":"Bakry-Émery Ricci Curvature Bounds for Doubly Warped Products of Weighted Spaces.","authors":"Zohreh Fathi,&nbsp;Sajjad Lakzian","doi":"10.1007/s12220-021-00745-7","DOIUrl":"https://doi.org/10.1007/s12220-021-00745-7","url":null,"abstract":"<p><p>We introduce a notion of doubly warped product of weighted graphs that is consistent with the doubly warped product in the Riemannian setting. We establish various discrete Bakry-Émery Ricci curvature-dimension bounds for such warped products in terms of the curvature of the constituent graphs. This requires deliberate analysis of the quadratic forms involved, prompting the introduction of some crucial notions such as curvature saturation at a vertex. In the spirit of being thorough and to provide a frame of reference, we also introduce the <math> <mfenced><msub><mi>R</mi> <mn>1</mn></msub> <mo>,</mo> <msub><mi>R</mi> <mn>2</mn></msub> </mfenced> </math> -doubly warped products of smooth measure spaces and establish <math><mi>N</mi></math> -Bakry-Émery Ricci curvature (lower) bounds thereof in terms of those of the factors. At the end of these notes, we present examples and demonstrate applications of warped products with some toy models.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"32 3","pages":"79"},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8753965/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39687129","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: 4
Exception Sets of Intrinsic and Piecewise Lipschitz Functions. 本征函数和片状 Lipschitz 函数的例外集。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2022-01-01 Epub Date: 2022-02-01 DOI: 10.1007/s12220-021-00860-5
Gunther Leobacher, Alexander Steinicke
{"title":"Exception Sets of Intrinsic and Piecewise Lipschitz Functions.","authors":"Gunther Leobacher, Alexander Steinicke","doi":"10.1007/s12220-021-00860-5","DOIUrl":"10.1007/s12220-021-00860-5","url":null,"abstract":"<p><p>We consider a class of functions defined on metric spaces which generalizes the concept of piecewise Lipschitz continuous functions on an interval or on polyhedral structures. The study of such functions requires the investigation of their exception sets where the Lipschitz property fails. The newly introduced notion of permeability describes sets which are natural exceptions for Lipschitz continuity in a well-defined sense. One of the main results states that continuous functions which are intrinsically Lipschitz continuous outside a permeable set are Lipschitz continuous on the whole domain with respect to the intrinsic metric. We provide examples of permeable sets in <math> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> </math> , which include Lipschitz submanifolds.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"32 4","pages":"118"},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8807473/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39914097","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
The Fundamental Solution to $$Box _b$$ on Quadric Manifolds: Part 3. Asymptotics for a Codimension 2 Case in $${mathbb {C}}^4$$ 二次流形$$Box _b$$的基本解:第3部分。中余维数2的渐近性 $${mathbb {C}}^4$$
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-05-26 DOI: 10.1007/S12220-021-00693-2
A. Boggess, A. Raich
{"title":"The Fundamental Solution to $$Box _b$$ on Quadric Manifolds: Part 3. Asymptotics for a Codimension 2 Case in $${mathbb {C}}^4$$","authors":"A. Boggess, A. Raich","doi":"10.1007/S12220-021-00693-2","DOIUrl":"https://doi.org/10.1007/S12220-021-00693-2","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S12220-021-00693-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42658630","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: 3
Discrete Subgroups of $$text{ PSL }(n+1,{mathbb {C}})$$ Acting on the Grassmannians $$text｛PSL｝（n+1，｛mathbb｛C｝｝）$$的离散子群作用于Grassmann
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-03-29 DOI: 10.1007/S12220-021-00651-Y
Haremy Zúñiga
{"title":"Discrete Subgroups of $$text{ PSL }(n+1,{mathbb {C}})$$ Acting on the Grassmannians","authors":"Haremy Zúñiga","doi":"10.1007/S12220-021-00651-Y","DOIUrl":"https://doi.org/10.1007/S12220-021-00651-Y","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-28"},"PeriodicalIF":1.1,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S12220-021-00651-Y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49335966","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
On Grünbaum Type Inequalities 关于<s:1> nbaum型不等式
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-03-16 DOI: 10.1007/s12220-021-00635-y
Francisco Marín Sola, J. Yepes Nicolás
{"title":"On Grünbaum Type Inequalities","authors":"Francisco Marín Sola, J. Yepes Nicolás","doi":"10.1007/s12220-021-00635-y","DOIUrl":"https://doi.org/10.1007/s12220-021-00635-y","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"31 1","pages":"9981 - 9995"},"PeriodicalIF":1.1,"publicationDate":"2021-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-021-00635-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52802572","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
A Modified Morrey-Kohn-Hörmander Identity and Applications to the $$overline{partial }$$-Problem A修改Morrey-Kohn-Hörmander身份及$$overline{partial }$$的应用-问题
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-02-27 DOI: 10.1007/S12220-021-00623-2
D. Chakrabarti, Phillip S. Harrington
{"title":"A Modified Morrey-Kohn-Hörmander Identity and Applications to the $$overline{partial }$$-Problem","authors":"D. Chakrabarti, Phillip S. Harrington","doi":"10.1007/S12220-021-00623-2","DOIUrl":"https://doi.org/10.1007/S12220-021-00623-2","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-38"},"PeriodicalIF":1.1,"publicationDate":"2021-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S12220-021-00623-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41562911","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
The Geometry of $$Phi _S$$-Harmonic Maps $$Phi _S$$的几何-调和映射
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-02-19 DOI: 10.1007/S12220-021-00612-5
S. Feng, Yingbo Han, Xiao Li, S. Wei
{"title":"The Geometry of $$Phi _S$$-Harmonic Maps","authors":"S. Feng, Yingbo Han, Xiao Li, S. Wei","doi":"10.1007/S12220-021-00612-5","DOIUrl":"https://doi.org/10.1007/S12220-021-00612-5","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-40"},"PeriodicalIF":1.1,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S12220-021-00612-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42941708","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: 2
Rotation Bounds for Hölder Continuous Homeomorphisms with Integrable Distortion 具有可积畸变的Hölder连续同胚的旋转界
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-02-17 DOI: 10.1007/s12220-022-00950-y
A. Clop, L. Hitruhin, B. Sengupta
{"title":"Rotation Bounds for Hölder Continuous Homeomorphisms with Integrable Distortion","authors":"A. Clop, L. Hitruhin, B. Sengupta","doi":"10.1007/s12220-022-00950-y","DOIUrl":"https://doi.org/10.1007/s12220-022-00950-y","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"32 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44367622","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
Compactness of Surfaces in $$pmb {mathbb {R}}^n$$ with Small Total Curvature 总曲率较小的$$pmb｛mathbb｛R｝｝^n$$表面压实度
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-02-05 DOI: 10.1007/S12220-020-00583-Z
Jianxin Sun, Jie Zhou
{"title":"Compactness of Surfaces in $$pmb {mathbb {R}}^n$$ with Small Total Curvature","authors":"Jianxin Sun, Jie Zhou","doi":"10.1007/S12220-020-00583-Z","DOIUrl":"https://doi.org/10.1007/S12220-020-00583-Z","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-33"},"PeriodicalIF":1.1,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S12220-020-00583-Z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47757234","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
$$C^k$$-Estimates for $$bar{partial }$$-Equation on Certain Convex Domains of Infinite Type in $$mathbb {C}^n$$ $$C^k$$无穷型凸域上的方程$$bar{partial }$$的估计 $$mathbb {C}^n$$
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-02-01 DOI: 10.1007/S12220-019-00332-X
L. Ha
{"title":"$$C^k$$-Estimates for $$bar{partial }$$-Equation on Certain Convex Domains of Infinite Type in $$mathbb {C}^n$$","authors":"L. Ha","doi":"10.1007/S12220-019-00332-X","DOIUrl":"https://doi.org/10.1007/S12220-019-00332-X","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"402 1","pages":"2058-2087"},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86831125","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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