The chord log-Minkowski problem for 0<𝑞<1

Qin, Lei

doi:10.1090/proc/16747

The chord log-Minkowski problem for $0<q<1$
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by Lei Qin

Proc. Amer. Math. Soc.

DOI: https://doi.org/10.1090/proc/16747

Published electronically: April 11, 2024

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Abstract:

The chord log-Minkowski problem asks for necessary and sufficient conditions for a finite Borel measure on the unit sphere so that it is the cone-chord measure of a convex body. The chord log-Minkowski problem has been extensively studied by Guo, Xi, and Zhao [Math. Ann. (2023), DOI 10.1007/s00208-023-02721-8]; Lutwak, Xi, Yang, and Zhang [Commun. Pure Appl. Math. (2023), DOI 10.1002/cpa.22190]; Qin [Adv. Math. 427 (2023), Paper No. 109132]. In this paper, we solve the chord log-Minkowski problem when $q\in (0,1)$, without symmetry assumptions.

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