Hessian measures of convex functions and applications to area measures

被引：9
|
作者：
Colesanti, A
Hug, D
机构：
[1] Univ Florence, Dipartimento Matemat, I-50134 Florence, Italy
[2] Univ Freiburg, Inst Math, D-79104 Freiburg, Germany
来源：
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2005年 / 71卷
关键词：
D O I：
10.1112/S0024610704005915
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Hessian measures of a (semi-)convex function can be introduced as coefficients of a local Steiner formula. The investigation of Hessian measures is continued by the provision of a geometric characterization of the support of these measures. Then the Radon-Nikodym derivative and the absolute continuity of Hessian measures with respect to Lebesgue measure are explored. As special cases of the results, known results for surface area measures of convex bodies are recovered.
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页码：221 / 235
页数：15
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