A proof of Alexandrov's uniqueness theorem for convex surfaces in R3
Annales de l'I.H.P. Analyse non linéaire, Volume 33 (2016) no. 2, pp. 329-336.

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.

DOI: 10.1016/j.anihpc.2014.09.011
Classification: 53A05, 53C24
Keywords: Uniqueness, Convex surfaces, Nonlinear elliptic equations, Unique continuation, Alexandrov theorem
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Guan, Pengfei; Wang, Zhizhang; Zhang, Xiangwen. A proof of Alexandrov's uniqueness theorem for convex surfaces in $ {\mathbb{R}}^{3}$. Annales de l'I.H.P. Analyse non linéaire, Volume 33 (2016) no. 2, pp. 329-336. doi : 10.1016/j.anihpc.2014.09.011. http://www.numdam.org/articles/10.1016/j.anihpc.2014.09.011/

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