Hausdorff volume in non equiregular sub-Riemannian manifolds

被引：7

作者：

Ghezzi, R. ^{[1
]}

Jean, F. ^{[2
]}

机构：

[1] Inst Math Bourgogne UBFC, F-21078 Dijon, France

[2] INRIA Saclay Ile de France, Team GECO, Palaiseau, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 126卷

基金：

欧洲研究理事会; 欧盟第七框架计划;

关键词：

Sub-Riemannian geometry; Hausdorff measures; Intrinsic volumes; Geometric measure theory; COMPLEXITY; FORMULA; ENTROPY;

D O I：

10.1016/j.na.2015.06.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it with a smooth volume. We first give the Lebesgue decomposition of the Hausdorff volume. Then we study the regular part, show that it is not commensurable with the smooth volume, and give conditions under which it is a Radon measure. We finally give a complete characterization of the singular part. We illustrate our results and techniques on numerous examples and cases (e.g. to generic sub-Riemannian structures). (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：345 / 377

页数：33

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