Mathematische Annalen

, Volume 347, Issue 3, pp 703–737 | Cite as

Inequalities for mixed p-affine surface area

  • Elisabeth WernerEmail author
  • Deping Ye


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 L p 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)

52A20 53A15 


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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

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