Hypersurfaces of prescribed curvature measure

Pengfei Guan, Junfang Li, Yanyan Li

Research output: Contribution to journalArticlepeer-review

59 Scopus citations

Abstract

We consider the corresponding Christoffel-Minkowski problem for curvature measures. The existence of star-shaped (n - k)-convex bodies with prescribed kth curvature measures (k > 0) has been a longstanding problem. This is settled in this paper through the establishment of a crucial a priori C 2-estimate for the corresponding curvature equation on S n.

Original languageEnglish (US)
Pages (from-to)1927-1942
Number of pages16
JournalDuke Mathematical Journal
Volume161
Issue number10
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • General Mathematics

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