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A Hopf theorem for open surfaces in product spaces
-
Manfredo do Carmo
Published/Copyright:
September 3, 2009
Abstract
Hopf's theorem has been recently extended to compact genus zero surfaces with constant mean curvature H in a product space 
, where 
is a surface with constant Gaussian curvature k ≠ 0 [Abresch, Rosenberg, Acta Math. 193: 141–174, 2004]. It also has been observed that, rather than H = const., it suffices to assume that the differential dH of H is appropriately bounded [Alencar, do Carmo, Tribuzy, Analysis Geometry 15: 283–298, 2007]. Here, we consider the case of simply-connected open surfaces with boundary in such that dH is appropriately bounded and certain conditions on the boundary are satisfied, and show that such surfaces can all be described.
Received: 2007-12-16
Revised: 2008-02-19
Published Online: 2009-09-03
Published in Print: 2009-November
© de Gruyter 2009
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Articles in the same Issue
- A Hopf theorem for open surfaces in product spaces
- On R. Steinberg's theorem on algebras of coinvariants
- Natural pseudo-distances between closed curves
- Clifford semigroups of ideals in monoids and domains
- Lp norm estimates of eigenfunctions restricted to submanifolds
- Central values of generalized multiple sine functions
- Lp-independence of spectral bounds of non-local Feynman-Kac semigroups
- On pairwise mutually permutable products
- The block structure spaces of real projective spaces and orthogonal calculus of functors II
- Erratum to: “Intrinsic ultracontractivity for non-symmetric Lévy processes” [Forum Math. 21 (2009) 43–66]
