A Hopf theorem for non-constant mean curvature and a conjecture of A. D. Alexandrov

作者：Galvez Jose A^*; Mira Pablo

来源：Mathematische Annalen, 2016, 366(3-4): 909-928.

DOI：10.1007/s00208-015-1351-4

We prove a uniqueness theorem for immersed spheres of prescribed (non-constant) mean curvature in homogeneous three-manifolds. In particular, this uniqueness theorem proves a conjecture by A. D. Alexandrov about immersed spheres of prescribed Weingarten curvature in for the special but important case of prescribed mean curvature. As a consequence, we extend the classical Hopf uniqueness theorem for constant mean curvature spheres to the case of immersed spheres of prescribed antipodally symmetric mean curvature in .

• 出版日期2016-12