Integral Geometric Regularity

被引：11

作者：

Fu, Joseph H. G. ^{[1
]}

机构：

[1] Univ Georgia, Dept Math, Athens, GA 30602 USA

来源：

TENSOR VALUATIONS AND THEIR APPLICATIONS IN STOCHASTIC GEOMETRY AND IMAGING | 2017年 / 2177卷

基金：

美国国家科学基金会;

关键词：

R-DIMENSIONAL BALLS; CURVATURE MEASURES; CHERN CLASSES; SETS; DIRECTIONS; DIAMETER; SURFACES; SEGMENTS; SMOOTH; CYCLES;

D O I：

10.1007/978-3-319-51951-7_10

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Smooth scalar-valued valuations may be thought of as curvature integrals that are robust enough to apply to objects with convex singularities. It turns out that certain kinds of nonconvex singularities are also included. The distinguishing feature is the existence of a normal cycle, which is an integral current that stands in for the manifold of unit normals in case they do not exist in the usual sense. We describe the elements of the normal cycle construction, and sketch how it may be used to establish the fundamental relations of integral geometry, with emphasis on the class of WDC sets recently introduced by Pokorny and Rataj.

引用

页码：261 / 299

页数：39

共 43 条

[1]

Alberti G, 1999, MATH Z, V230, P259, DOI 10.1007/PL00004691

[2] Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture [J].