卡诺群上的特殊测度族

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2022-09-18 DOI:10.1515/agms-2022-0148

B. Franchi, I. Markina

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引用次数: 0

摘要

摘要研究了具有消失p p -模的卡诺群上的测度族，我们称之为M p {M＿p} -{例外族。我们得到了通过一个公共点的本征Lipschitz曲面族为M p M＿p的充分必要条件- }p{≥1 p }{}\ge 1{例外}。对于p∈(0，∞)p {}\in\left (0, \infty)，我们描述了一类广义的M p M＿p -例外内禀Lipschitz曲面。

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Exceptional families of measures on Carnot groups

Abstract We study the families of measures on Carnot groups that have vanishing p p -module, which we call M p {M}_{p} -exceptional families. We found necessary and sufficient Conditions for the family of intrinsic Lipschitz surfaces passing through a common point to be M p {M}_{p} -exceptional for p ≥ 1 p\ge 1 . We describe a wide class of M p {M}_{p} -exceptional intrinsic Lipschitz surfaces for p ∈ ( 0 , ∞ ) p\in \left(0,\infty ) .

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.