A proof of Alexandrov's uniqueness theorem for convex surfaces in $ R^{3} $

Pengfei Guan; Zhizhang Wang; Xiangwen Zhang

doi:10.1016/j.anihpc.2014.09.011

JournalsaihpcVol. 33, No. 2pp. 329–336

A proof of Alexandrov's uniqueness theorem for convex surfaces in $R^{3}$

Pengfei Guan
Department of Mathematics and Statistics, McGill University, Montreal, Canada
Zhizhang Wang
Department of Mathematics, Fudan University, Shanghai, China
Xiangwen Zhang
Department of Mathematics, Columbia University, New York, United States

$A proof of Alexandrov's uniqueness theorem for convex surfaces in $ R^{3} $ cover$

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Abstract

We give a new proof of a classical uniqueness theorem of Alexandrov [4] using the weak uniqueness continuation theorem of Bers–Nirenberg [8]. 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.

Cite this article

Pengfei Guan, Zhizhang Wang, Xiangwen Zhang, A proof of Alexandrov's uniqueness theorem for convex surfaces in $R^{3}$ . Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 2, pp. 329–336

DOI 10.1016/J.ANIHPC.2014.09.011