A proof of the Alexanderov's uniqueness theorem for convex surfaces in $\mathbb R^3$

Pengfei Guan; Zhizhang Wang; Xiangwen Zhang

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arXiv · 1305.0077

A proof of the Alexanderov's uniqueness theorem for convex surfaces in $\mathbb R^3$

Pengfei Guan·Zhizhang Wang·Xiangwen Zhang

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Abstract

We give a new proof of a classical uniqueness theorem of Alexandrov using the weak uniqueness continuation theorem of Bers-Nirenberg. We prove a version of this theorem with the minimal regularity assumption: the spherical hessians of the corresponding convex bodies as Radon measures are nonsingular.

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Pengfei Guan, Zhizhang Wang, Xiangwen Zhang. 2013-05-01. A proof of the Alexanderov's uniqueness theorem for convex surfaces in $\mathbb R^3$. https://arxiv.org/abs/1305.0077

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