On Minimizing Problems with a Volume Constraint in Hyperbolic 3-Manifolds |
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Authors: | Masahito Toda |
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Institution: | (1) Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo, 192-03, Japan (E-mail |
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Abstract: | This paper investigates the existence of an area (or Dirichlet integral) minimizing parametric surface in a hyperbolic 3-manifold subject to a volume constraint. The existence of a minimizing surface is proved, assuming some conditions on the prescribed free homotopy class. This result implies a non-existence result of minimizing surfaces of prescribed mean curvature. A criterion for the existence of surfaces of prescribed mean curvature, which turns out to be optimal in view of the non-existence result, is also obtained. |
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Keywords: | surface of constant mean curvature variational problem with a constraint |
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