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HESSIAN MEASURES OF CONVEX FUNCTIONS AND APPLICATIONS TO AREA MEASURES

Published online by Cambridge University Press:  04 February 2005

ANDREA COLESANTI  and
DANIEL HUG
ANDREA COLESANTI
Affiliation:
Dipartimento di Matematica, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italyandrea.colesanti@math.unifi.it
DANIEL HUG
Affiliation:
Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstrasse 1, D-79104 Freiburg, Germanydaniel.hug@math.uni-freiburg.de
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Abstract

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.

Keywords

52A20 (primary)26B2528A78 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 71 , Issue 1 , February 2005 , pp. 221 - 235
Copyright
The London Mathematical Society 2005

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