Lp dual curvature measures

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Abstract

A new family of geometric Borel measures on the unit sphere is introduced. Special cases include the Lp surface area measures (which extend the classical surface area measure of Aleksandrov and Fenchel & Jessen) and Lp-integral curvature (which extends Alkesandrov's integral curvature) in the Lp Brunn–Minkowski theory. It also includes the dual curvature measures (which are the duals of Federer's curvature measures) in the dual Brunn–Minkowski theory. This partially unifies the classical theory of mixed volumes and the newer theory of dual mixed volumes.

Original languageEnglish (US)
Pages (from-to)85-132
Number of pages48
JournalAdvances in Mathematics
Volume329
DOIs
StatePublished - Apr 30 2018

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Keywords

  • Alexandrov problem
  • Dual Brunn–Minkowski theory
  • Dual curvature measures
  • Integral curvature
  • L Brunn–Minkowski theory
  • L-Minkowski problem

ASJC Scopus subject areas

  • Mathematics(all)

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