Abstract
The dual Minkowski problem for even data asks what are the necessary and sufficient conditions on a prescribed even measure on the unit sphere for it to be the q-th dual curvature measure of an origin-symmetric convex body in Rn. A full solution to this is given when 1<q<n. The necessary and sufficient conditions turn out to be an explicit measure concentration condition. To obtain the results, a variational approach is used, where the functional is the sum of a dual quermassintegral and an entropy integral. The proof requires two crucial estimates. The first is an estimate of the entropy integral which is obtained by using a spherical partition. The second is a sharp estimate of the dual quermassintegrals for a carefully chosen barrier convex body.
Original language | English (US) |
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Article number | 106805 |
Journal | Advances in Mathematics |
Volume | 356 |
DOIs | |
State | Published - Nov 7 2019 |
Keywords
- Convex body
- Dual Minkowski problem
- Minkowski problem
- Radial Gauss image
- Subspace concentration condition
ASJC Scopus subject areas
- General Mathematics