Hypersurfaces of Prescribed Curvature Measure

Details Hypersurfaces of Prescribed Curvature Measure Hypersurfaces of Prescribed Curvature Measure

2011-03-11

arxiv.org/abs/1103.2383v1

Mathematics

Differential Geometry

Scientific paper

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 ($k>0$) has been a longstanding problem. This is
settled in this paper through the establishment of a crucial $C^2$ a priori
estimate for the corresponding curvature equation on $\mathbb S^n$.

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