Existence of Solutions to $L_p$-Gaussian Minkowski problem
Shengyu Tang
TL;DR
This paper proves the existence of solutions with small volume for the $L_p$-Gaussian Minkowski problem when 1 ≤ p < n, indicating multiple solutions exist for this geometric problem.
Contribution
It establishes the existence of solutions with small volume for the $L_p$-Gaussian Minkowski problem and shows there are at least two solutions in this setting.
Findings
Existence of small volume solutions for the $L_p$-Gaussian Minkowski problem.
Multiple solutions exist for the problem when 1 ≤ p < n.
Abstract
In this paper, we derive the existence of solutions with small volume to the -Gaussian Minkowski problem for , which implies that there are at least two solutions for the -Gaussian Minkowski problem.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows · Geology and Paleoclimatology Research