Smooth solutions to the Lp dual Minkowski problem

Chuanqiang Chen; Yong Huang; Yiming Zhao

doi:10.1007/s00208-018-1727-3

Smooth solutions to the L_p dual Minkowski problem

Chuanqiang Chen, Yong Huang, Yiming Zhao

Research output: Contribution to journal › Article › peer-review

58 Scopus citations

Abstract

In this paper, we consider the L_p dual Minkowski problem by geometric variational method. Using anisotropic Gauss–Kronecker curvature flows, we establish the existence of smooth solutions of the L_p dual Minkowski problem when pq≥ 0 and the given data is even. If f≡ 1 , we show under some restrictions on p and q that the only even, smooth, uniformly convex solution is the unit ball.

Original language	English (US)
Pages (from-to)	953-976
Number of pages	24
Journal	Mathematische Annalen
Volume	373
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-018-1727-3
State	Published - Apr 1 2019
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/s00208-018-1727-3

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title = "Smooth solutions to the Lp dual Minkowski problem",

abstract = "In this paper, we consider the Lp dual Minkowski problem by geometric variational method. Using anisotropic Gauss–Kronecker curvature flows, we establish the existence of smooth solutions of the Lp dual Minkowski problem when pq≥ 0 and the given data is even. If f≡ 1 , we show under some restrictions on p and q that the only even, smooth, uniformly convex solution is the unit ball.",

author = "Chuanqiang Chen and Yong Huang and Yiming Zhao",

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N2 - In this paper, we consider the Lp dual Minkowski problem by geometric variational method. Using anisotropic Gauss–Kronecker curvature flows, we establish the existence of smooth solutions of the Lp dual Minkowski problem when pq≥ 0 and the given data is even. If f≡ 1 , we show under some restrictions on p and q that the only even, smooth, uniformly convex solution is the unit ball.

AB - In this paper, we consider the Lp dual Minkowski problem by geometric variational method. Using anisotropic Gauss–Kronecker curvature flows, we establish the existence of smooth solutions of the Lp dual Minkowski problem when pq≥ 0 and the given data is even. If f≡ 1 , we show under some restrictions on p and q that the only even, smooth, uniformly convex solution is the unit ball.

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Smooth solutions to the L_p dual Minkowski problem

Abstract

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