A theorem of Hopf and the Cauchy-Riemann inequality

Hilário Alencar, Manfredo do Carmo, Renato Tribuzy

Type: Article

Publication Date: 2007-01-01

Citations: 21

DOI: https://doi.org/10.4310/cag.2007.v15.n2.a3

Abstract

have extended Hopf's Theorem on constant mean curvature to 3-dimensional spaces other than the space forms.Here we show that, rather than assuming constant mean curvature, it suffices to assume an inequality on the differential of the mean curvature.

Locations

Communications in Analysis and Geometry - View - PDF

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+ PDF Chat	Maximum principle for semi-elliptic trace operators and geometric applications	2014	G. Pacelli Bessa Leandro F. Pessoa
+	Some Recent Developments on Hopf’s Holomorphic Form	2011	Manfredo P. do Carmo
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+ PDF Chat	A Hopf theorem for non-constant mean curvature and a conjecture of A. D. Alexandrov	2015	José A. Gálvez Pablo Mira
+	A Hopf theorem for open surfaces in product spaces	2012	Manfredo do Carmo Isabel Fernández

Works Cited by This (4)

Action	Title	Year	Authors
+	Complex analysis and a class of Weingarten surfaces	2011	Robert L. Bryant
+	Some new characterizations of the Euclidean sphere	1945	Shiing-Shen Chern
+	On the Local Behavior of Solutions of Non-Parabolic Partial Differential Equations	1953	Philip Hartman Aurel Wintner
+	Differential Geometry in the Large	1983	Heinz Hopf