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On Discrete Constant Mean Curvature Surfaces

Discrete & Computational Geometry, 2014
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Hypersurfaces of Constant Mean Curvature

1989
I want to discuss some aspects of the theory of hypersurfaces of constant mean curvature H. The subject is intimately related to the theory of minimal hypersurfaces which corresponds to the case H = 0. There are, however, some striking differences between the two cases, and this can already be made clear in the simplest situation of surfaces in the ...
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Constant (nonlocal) Mean curvature surfaces

2021
The notion of Nonlocal Mean Curvature (NMC) appears recently in the mathematics literature. Alike their local counterpart, it is an extrinsic geometric quantity that is invariant under global reparameterization of a surface and provide a natural extension of the classical mean curvature.
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Constant Mean Curvature Tori

1991
Constant mean curvature tori in ℝ3 were first discovered, in 1984, by Wente [15]. These examples solved the long standing problem of Hopf [6]: Is a compact constant mean curvature surface in ℝ3 necessarily a round sphere? Hopf proved that if the surface is topologically a sphere then it must be round and Alexandrov [3] proved that if the surface is ...
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Constant Mean Curvature Surfaces in Hyperbolic Space

American Journal of Mathematics, 1992
The authors study the global geometry of complete, proper surfaces in hyperbolic \((n+1)\)-space with constant curvature \(>n\). Main results are, that such are never closed surfaces with only one puncture. If they have two punctures that are Delaunay cylinders, and if they have 3 punctures they remain a bounded distance from a geodesic plane.
KOREVAAR, NJ, KUSNER, R, MEEKS, WH, SOLOMON, B   +3 more
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