Hypersurfaces of prescribed curvature measure
Pengfei Guan, Junfang Li, and YanYan Li
Source: Duke Math. J. Volume 161, Number 10
(2012), 1927-1942.
Abstract
We consider the corresponding Christoffel–Minkowski problem for curvature measures. The existence of star-shaped $(n-k)$-convex bodies with prescribed $k$th curvature measures ($k\textgreater 0$) 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 $\mathbb{S}^{n}$.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1340801627
Digital Object Identifier: doi:10.1215/00127094-1645550
Zentralblatt MATH identifier: 06063224
Mathematical Reviews number (MathSciNet): MR2954620
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