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arXiv · 2502.05436

Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems

Yong Huang·Erwin Lutwak·Deane Yang·Gaoyong Zhang
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Abstract

A longstanding question in the dual Brunn-Minkowski theory is what are the dual analogues of Federer's curvature measures for convex bodies. The answer to this is provided. This leads naturally to dual versions of Minkowski-type problems, which answer the question of what are necessary and sufficient conditions for a Borel measure to be a dual curvature measure of a convex body. Sufficient conditions, involving measure concentration, are established for the existence of solutions to these problems.

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Yong Huang, Erwin Lutwak, Deane Yang, Gaoyong Zhang. 2025-02-08. Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems. https://doi.org/10.1007/s11511-016-0140-6

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