Continuity of the solution to the dual Minkowski problem for negative indices

Wang, Hejun; Fang, Niufa; Zhou, Jiazu

doi:10.1090/proc/13995

Continuity of the solution to the dual Minkowski problem for negative indices
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by Hejun Wang, Niufa Fang and Jiazu Zhou PDF

Proc. Amer. Math. Soc. 147 (2019), 1299-1312 Request permission

Abstract:

This paper concerns the continuity of the solution to the dual Minkowski problem for negative indices. For each $q<0$, it is proved that the weak convergence of $q$th dual curvature measures implies the convergence of the corresponding convex bodies in the Hausdorff metric and that the solution to the dual Minkowski problem is continuous with respect to $q$.

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