The LP-Aleksandrov problem for LP-integral curvature

Yong Huang, Erwin Lutwak, Deane Yang, Gaoyong Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

It is shown that within the Lp-Brunn–Minkowski theory that Aleksandrov’s integral curvature has a natural Lp extension, for all real p. This raises the question of finding necessary and sufficient conditions on a given measure in order for it to be the Lp-integral curvature of a convex body. This problem is solved for positive p and is answered for negative p provided the given measure is even.

Original languageEnglish (US)
Pages (from-to)1-29
Number of pages29
JournalJournal of Differential Geometry
Volume110
Issue number1
DOIs
StatePublished - Sep 2018

Keywords

  • Aleksandrov problem
  • And phrases. Curvature measure
  • Integral curvature
  • Lp-Aleksandrov problem
  • Lp-Minkowski problem
  • Lp-integral curvature
  • Minkowski problem
  • Surface area measure

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Fingerprint

Dive into the research topics of 'The L<sub>P</sub>-Aleksandrov problem for L<sub>P</sub>-integral curvature'. Together they form a unique fingerprint.

Cite this