A proof of Alexandrov's uniqueness theorem for convex surfaces in R-3

作者：Guan, Pengfei^*; Wang, Zhizhang; Zhang, Xiangwen

来源：ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2016, 33(2): 329-336.

DOI：10.1016/j.anihpc.2014.09.011

• Uniqueness
• Convex surfaces
• Nonlinear elliptic equations
• Unique continuation
• Alexandrov theorem

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.

• 出版日期2016-4
• 单位McGill; 复旦大学