The LP-Aleksandrov problem for LP-integral curvature

Research output: Contribution to journalArticle

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
StatePublished - Sep 1 2018

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Curvature
Convex Body
Necessary Conditions
Sufficient Conditions

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

The LP-Aleksandrov problem for LP-integral curvature. / Huang, Yong; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong.

In: Journal of Differential Geometry, Vol. 110, No. 1, 01.09.2018, p. 1-29.

Research output: Contribution to journalArticle

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