On The Minkowski Problem With Respect To A Mixed Euclidean-Gaussian Density

Stephanie Mui; Lei Qin; Sinan Wang

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arXiv · 2607.27618

On The Minkowski Problem With Respect To A Mixed Euclidean-Gaussian Density

Stephanie Mui·Lei Qin·Sinan Wang

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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-Amp\`{e}re-type equation in the symmetric case. Then, by approximation, we obtain the existence of origin-symmetric solutions to the mixed Euclidean-Gaussian Minkowski problem.

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Stephanie Mui, Lei Qin, Sinan Wang. 2026-07-30. On The Minkowski Problem With Respect To A Mixed Euclidean-Gaussian Density. https://arxiv.org/abs/2607.27618

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