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.
Keywords: Uniqueness, Convex surfaces, Nonlinear elliptic equations, Unique continuation, Alexandrov theorem
@article{AIHPC_2016__33_2_329_0, author = {Guan, Pengfei and Wang, Zhizhang and Zhang, Xiangwen}, title = {A proof of {Alexandrov's} uniqueness theorem for convex surfaces in $ {\mathbb{R}}^{3}$}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {329--336}, publisher = {Elsevier}, volume = {33}, number = {2}, year = {2016}, doi = {10.1016/j.anihpc.2014.09.011}, zbl = {1335.53092}, mrnumber = {3465378}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2014.09.011/} }
TY - JOUR AU - Guan, Pengfei AU - Wang, Zhizhang AU - Zhang, Xiangwen TI - A proof of Alexandrov's uniqueness theorem for convex surfaces in $ {\mathbb{R}}^{3}$ JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 329 EP - 336 VL - 33 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2014.09.011/ DO - 10.1016/j.anihpc.2014.09.011 LA - en ID - AIHPC_2016__33_2_329_0 ER -
%0 Journal Article %A Guan, Pengfei %A Wang, Zhizhang %A Zhang, Xiangwen %T A proof of Alexandrov's uniqueness theorem for convex surfaces in $ {\mathbb{R}}^{3}$ %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 329-336 %V 33 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2014.09.011/ %R 10.1016/j.anihpc.2014.09.011 %G en %F AIHPC_2016__33_2_329_0
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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