Duke Mathematical Journal

Hypersurfaces of prescribed curvature measure

Pengfei Guan, Junfang Li, and YanYan Li

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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.

Article information

Source
Duke Math. J., Volume 161, Number 10 (2012), 1927-1942.

Dates
First available in Project Euclid: 27 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1340801627

Digital Object Identifier
doi:10.1215/00127094-1645550

Mathematical Reviews number (MathSciNet)
MR2954620

Zentralblatt MATH identifier
1254.53073

Subjects
Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 35J60: Nonlinear elliptic equations 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Citation

Guan, Pengfei; Li, Junfang; Li, YanYan. Hypersurfaces of prescribed curvature measure. Duke Math. J. 161 (2012), no. 10, 1927--1942. doi:10.1215/00127094-1645550. https://projecteuclid.org/euclid.dmj/1340801627


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