The Lp Minkowski problem for polytopes for 0 < p < 1
Guangxian Zhu
TL;DR
This paper establishes necessary and sufficient conditions for solving the discrete Lp Minkowski problem specifically for polytopes when 0 < p < 1, advancing understanding in convex geometry.
Contribution
It provides the first complete characterization of solutions to the discrete Lp Minkowski problem in the critical range 0 < p < 1 for polytopes.
Findings
Necessary and sufficient conditions for solutions are identified.
The results apply specifically to polytopes in the critical p-range.
Advances the theoretical understanding of the Lp Minkowski problem.
Abstract
Necessary and sufficient conditions are given for the existence of solutions to the discrete Lp Minkowski problem for the critical case where 0 < p < 1.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows · Diffusion and Search Dynamics