A proof of the Alexanderov's uniqueness theorem for convex surfaces in \mathbb R³

2013/05/01 by Pengfei Guan, Zhizhang Wang, Guan, Pengfei +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1305.0077

openalex publication_date 2013/05/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• On the solutions of quasi-linear elliptic partial differential equations

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