On the Lp dual Minkowski problem

Yong Huang, Yiming Zhao

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

The Lp dual curvature measure was introduced by Lutwak, Yang & Zhang in an attempt to unify the Lp Brunn–Minkowski theory and the dual Brunn–Minkowski theory. The characterization problem for Lp dual curvature measure, called the Lp dual Minkowski problem, is a fundamental problem in this unifying theory. The Lp dual Minkowski problem contains the Lp Minkowski problem and the dual Minkowski problem, two major problems in modern convex geometry that remain open in general. In this paper, existence results on the Lp dual Minkowski problem in the weak sense will be provided. Moreover, existence and uniqueness of the solution in the smooth category will also be demonstrated.

Original languageEnglish (US)
Pages (from-to)57-84
Number of pages28
JournalAdvances in Mathematics
Volume332
DOIs
StatePublished - Jul 9 2018
Externally publishedYes

Keywords

  • Degenerate Monge–Ampère equation
  • Dual Minkowski problem
  • L dual Minkowski problem
  • L Minkowski problem
  • Regularity

ASJC Scopus subject areas

  • Mathematics(all)

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