Journal of Geometric Analysis最新文献_第2页

Hermitian-Yang-Mills Connections on Collapsing Elliptically Fibered K3 Surfaces. 塌缩椭圆纤维K3曲面上的Hermitian-Yang-Mills连接。

IF 1.1 2区数学

Journal of Geometric Analysis Pub Date : 2022-01-01 Epub Date: 2022-01-07 DOI: 10.1007/s12220-021-00808-9

Ved Datar, Adam Jacob

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引用次数: 2

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, Andrea Merlo","doi":"10.1007/s12220-022-00971-7","DOIUrl":"https://doi.org/10.1007/s12220-022-00971-7","url":null,"abstract":"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 h-lower density and finite h-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 h-density whenever the tangents admit at least one complementary subgroup.","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"32 9","pages":"239"},"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

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

引用次数: 0

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

引用次数: 4

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

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

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

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

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

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

引用次数: 1