Journal of Geometric Analysis最新文献

筛选
英文 中文
On Rectifiable Measures in Carnot Groups: Existence of Density. 卡诺群中的可校正测度:密度的存在性。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2022-01-01 Epub Date: 2022-07-18 DOI: 10.1007/s12220-022-00971-7
Gioacchino Antonelli, Andrea Merlo
{"title":"On Rectifiable Measures in Carnot Groups: Existence of Density.","authors":"Gioacchino Antonelli,&nbsp;Andrea Merlo","doi":"10.1007/s12220-022-00971-7","DOIUrl":"https://doi.org/10.1007/s12220-022-00971-7","url":null,"abstract":"<p><p>In this paper, we start a detailed study of a new notion of rectifiability in Carnot groups: we say that a Radon measure is <math><msub><mi>P</mi> <mi>h</mi></msub> </math> -rectifiable, for <math><mrow><mi>h</mi> <mo>∈</mo> <mi>N</mi></mrow> </math> , if it has positive <i>h</i>-lower density and finite <i>h</i>-upper density almost everywhere, and, at almost every point, it admits a unique tangent measure up to multiples. First, we compare <math><msub><mi>P</mi> <mi>h</mi></msub> </math> -rectifiability with other notions of rectifiability previously known in the literature in the setting of Carnot groups, and we prove that it is strictly weaker than them. Second, we prove several structure properties of <math><msub><mi>P</mi> <mi>h</mi></msub> </math> -rectifiable measures. Namely, we prove that the support of a <math><msub><mi>P</mi> <mi>h</mi></msub> </math> -rectifiable measure is almost everywhere covered by sets satisfying a cone-like property, and in the particular case of <math><msub><mi>P</mi> <mi>h</mi></msub> </math> -rectifiable measures with complemented tangents, we show that they are supported on the union of intrinsically Lipschitz and differentiable graphs. Such a covering property is used to prove the main result of this paper: we show that a <math><msub><mi>P</mi> <mi>h</mi></msub> </math> -rectifiable measure has almost everywhere positive and finite <i>h</i>-density whenever the tangents admit at least one complementary subgroup.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9293879/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40534631","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: 9
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信