On The Minkowski Problem With Respect To A Mixed Euclidean-Gaussian Density
arXiv:2607.27618
summary
The paper introduces a new type of Minkowski problem involving a mixed Euclidean-Gaussian volume and proves the existence of smooth, origin‑symmetric solutions using flow methods and approximation.
Abstract
In this paper, we pose a new class of Minkowski problems corresponding to the mixed Euclidean-Gaussian volume. Using the flow method, we prove the existence of smooth normalized solutions for the corresponding Monge-Ampère-type equation in the symmetric case. Then, by approximation, we obtain the existence of origin-symmetric solutions to the mixed Euclidean-Gaussian Minkowski problem.
Topics & keywords
#minkowski problem#mixed euclidean-gaussian volume#monge-ampere equation#flow method#origin-symmetric solutionsMinkowski problemEuclidean-Gaussian densityMonge‑Ampèregeometric flowsymmetry