We consider the corresponding Christoffel–Minkowski problem for curvature measures. The existence of star-shaped -convex bodies with prescribed th curvature measures () has been a longstanding problem. This is settled in this paper through the establishment of a crucial a priori -estimate for the corresponding curvature equation on .
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