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

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• 作者：Pengfei Guan^a ; ¹ ; ^{guan@math.mcgill.ca" class="auth_mail" title="E-mail the corresponding author} ; Zhizhang Wang^b ; ^{zwang@math.mcgill.ca" class="auth_mail" title="E-mail the corresponding author} ; Xiangwen Zhang^c ; ^{xzhang@math.columbia.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：53A05 ; 53C24
• 刊名：Annales de l'Institut Henri Poincare (C) Non Linear Analysis
• 出版年：2016
• 出版时间：March-April 2016
• 年：2016
• 卷：33
• 期：2
• 页码：329-336
• 全文大小：282 K

文摘

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.