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)|
|Number of pages||16|
|Journal||Duke Mathematical Journal|
|State||Published - 2012|
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