A proof of Alexandrov's uniqueness theorem for convex surfaces in $ {\mathbb{R}}^{3}$

Guan, Pengfei; Wang, Zhizhang; Zhang, Xiangwen

doi:10.1016/j.anihpc.2014.09.011

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

R^{3}

Guan, Pengfei ; Wang, Zhizhang ; Zhang, Xiangwen

Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 2, pp. 329-336

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Résumé

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.

MR Zbl

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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     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://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.09.011/}
}

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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, Tome 33 (2016) no. 2, pp. 329-336. doi: 10.1016/j.anihpc.2014.09.011

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