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Area-minimizing disks with free boundary and prescribed enclosed volume
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Wolfram Bürger
Published/Copyright:
July 1, 2008
Abstract
For a set Ω ⊂ ℝ3 which is diffeomorphic to a ball, we consider the problem of minimizing the area in the class of parametrized disks enclosing a prescribed volume with ∂Ω. Here the volume is defined only up to integer multiples of 
3(Ω) for topological reasons. We prove that the infimum is always realized by a system of finitely many disks, each of which is a parametric H-surface meeting ∂Ω orthogonally along its boundary.
Received: 2006-01-19
Published Online: 2008-07-01
Published in Print: 2008-August
© Walter de Gruyter Berlin · New York 2008
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Articles in the same Issue
- Area-minimizing disks with free boundary and prescribed enclosed volume
- Isomorphisms between topological conjugacy algebras
- Hybrid bounds for twisted L-functions
- Symmetric norms and spaces of operators
- Fourier-Laplace transform of a variation of polarized complex Hodge structure
- Geometrization of the Strong Novikov Conjecture for residually finite groups
- The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras
- Complete reducibility and commuting subgroups
