Hypersurfaces of prescribed curvature measure

Pengfei Guan; Junfang Li; Yanyan Li

doi:10.1215/00127094-1645550

Hypersurfaces of prescribed curvature measure

Pengfei Guan, Junfang Li, Yanyan Li

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

40 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 language	English (US)
Pages (from-to)	1927-1942
Number of pages	16
Journal	Duke Mathematical Journal
Volume	161
Issue number	10
DOIs	https://doi.org/10.1215/00127094-1645550
State	Published - 2012

All Science Journal Classification (ASJC) codes

Mathematics(all)

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title = "Hypersurfaces of prescribed curvature measure",

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.",

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AU - Li, Yanyan

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AB - 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.

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DO - 10.1215/00127094-1645550

M3 - Article

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VL - 161

SP - 1927

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JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 10

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Hypersurfaces of prescribed curvature measure

Abstract

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