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On the Lp Gaussian Minkowski problem

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arxiv 2211.10956 v1 pith:OFXVX3RB submitted 2022-11-20 math.AP math.DG

Yibin Feng , Shengnan Hu , Lei Xu This is my paper · ORCID
classification math.APmath.DG
keywords gaussianproblemexistenceminkowskirespsolutionswillasymmetric
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abstract

Existence of symmetric (resp. asymmetric) solutions to the $L_p$ Gaussian Minkowski problem for $p\leq 0$ (resp. $p\geq 1$) will be provided. Moreover, existence and uniqueness of smooth solutions to the problem for $p>n$ will also be proved without the restriction that the Gaussian volumes of convex bodies are not less than one-second.

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  1. Minkowski Problems for Geometric Measures

    math.MG 2025-02 unverdicted novelty 2.0 of 10

    A comprehensive survey that organizes the Minkowski problems of convex geometry into a unified framework based on geometric measures as differentials of global geometric invariants.

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