Inequalities for mixed p-affine surface area

Elisabeth Werner, Deping Ye

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)703-737
Number of pages35
JournalMathematische Annalen
Issue number3
StatePublished - 2010
Externally publishedYes

Bibliographical note

Funding Information:
E. Werner was partially supported by an NSF grant, a FRG-NSF grant and a BSF grant.


  • 52A20
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