On the 𝐿_{𝑝}-Minkowski problem

Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong

doi:10.1090/S0002-9947-03-03403-2

On the $L_{p}$-Minkowski problem
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by Erwin Lutwak, Deane Yang and Gaoyong Zhang

Trans. Amer. Math. Soc. 356 (2004), 4359-4370

DOI: https://doi.org/10.1090/S0002-9947-03-03403-2

Published electronically: December 15, 2003

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Abstract:

A volume-normalized formulation of the $L_{p}$-Minkowski problem is presented. This formulation has the advantage that a solution is possible for all $p\ge 1$, including the degenerate case where the index $p$ is equal to the dimension of the ambient space. A new approach to the $L_{p}$-Minkowski problem is presented, which solves the volume-normalized formulation for even data and all $p\ge 1$.

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