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15 July 2012 Hypersurfaces of prescribed curvature measure
Pengfei Guan, Junfang Li, YanYan Li
Duke Math. J. 161(10): 1927-1942 (15 July 2012). DOI: 10.1215/00127094-1645550

Abstract

We consider the corresponding Christoffel–Minkowski problem for curvature measures. The existence of star-shaped (nk)-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 C2-estimate for the corresponding curvature equation on Sn.

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Pengfei Guan. Junfang Li. YanYan Li. "Hypersurfaces of prescribed curvature measure." Duke Math. J. 161 (10) 1927 - 1942, 15 July 2012. https://doi.org/10.1215/00127094-1645550

Information

Published: 15 July 2012
First available in Project Euclid: 27 June 2012

zbMATH: 1254.53073
MathSciNet: MR2954620
Digital Object Identifier: 10.1215/00127094-1645550

Subjects:
Primary: 53C23
Secondary: 35J60, 53C42

Rights: Copyright © 2012 Duke University Press

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Vol.161 • No. 10 • 15 July 2012
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