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

A proof of Alexandrov's uniqueness theorem for convex surfaces in R3 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 R3 R^{3} . Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 2, pp. 329–336

DOI 10.1016/J.ANIHPC.2014.09.011