Mathematische Annalen

, Volume 347, Issue 3, pp 703–737

Inequalities for mixed p-affine surface area

Article

DOI: 10.1007/s00208-009-0453-2

Cite this article as:
Werner, E. & Ye, D. Math. Ann. (2010) 347: 703. doi:10.1007/s00208-009-0453-2

Abstract

We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed p-affine surface areas. We introduce a new class of bodies, the illumination surface bodies, and establish some of their properties. We show, for instance, that they are not necessarily convex. We give geometric interpretations of Lp affine surface areas, mixed p-affine surface areas and other functionals via these bodies. The surprising new element is that not necessarily convex bodies provide the tool for these interpretations.

Mathematics Subject Classification (2000)

52A2053A15

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsCase Western Reserve UniversityClevelandUSA
  2. 2.UFR de Mathématique, Université de Lille 1Villeneuve d’AscqFrance