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The Minkowski problem for the non-compact convex set with an asymptotic boundary condition
- Publication Year :
- 2024
-
Abstract
- In this paper, combining the covolume, we study the Minkowski theory for the non-compact convex set with an asymptotic boundary condition. In particular, the mixed covolume of two non-compact convex sets is introduced and its geometric interpretation is obtained by the Hadamard variational formula. The Brunn-Minkowski and Minkowski inequalities for covolume are established, and the equivalence of these two inequalities are discussed as well. The Minkowski problem for non-compact convex set is proposed and solved under the asymptotic conditions. In the end, we give a solution to the Minkowski problem for $\sigma$-finite measure on the conic domain $\Omega_C$.<br />Comment: 20 pages
- Subjects :
- Mathematics - Differential Geometry
52B45, 52A20, 52A39, 53A15
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2402.12802
- Document Type :
- Working Paper