Inequalities for mixed p-affine surface area

Elisabeth Werner, Deping Ye

Research output: Contribution to journalArticlepeer-review

52 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)703-737
Number of pages35
JournalMathematische Annalen
Volume347
Issue number3
DOIs
StatePublished - Jan 1 2010

Keywords

  • 52A20
  • 53A15

Fingerprint Dive into the research topics of 'Inequalities for mixed p-affine surface area'. Together they form a unique fingerprint.

Cite this