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Genus bounds for minimal surfaces arising from min-max constructions
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Camillo De Lellis
Published/Copyright:
May 31, 2010
Abstract
In this paper we prove genus bounds for closed embedded minimal surfaces in a closed 3-dimensional manifold constructed via min-max arguments. A stronger estimate was announced by Pitts and Rubinstein but to our knowledge its proof has never been published. Our proof follows ideas of Simon and uses an extension of a famous result of Meeks, Simon and Yau on the convergence of minimizing sequences of isotopic surfaces. This result is proved in the second part of the paper.
Received: 2008-10-30
Published Online: 2010-05-31
Published in Print: 2010-July
© Walter de Gruyter Berlin · New York 2010
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- Arithmetic homology and an integral version of Kato's conjecture
- Small groups of finite Morley rank with involutions
- Genus bounds for minimal surfaces arising from min-max constructions
- Iterative q-difference Galois theory
- Conic-connected manifolds
- A visible factor of the special L-value
- Modular Galois covers associated to symplectic resolutions of singularities
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Articles in the same Issue
- Arithmetic homology and an integral version of Kato's conjecture
- Small groups of finite Morley rank with involutions
- Genus bounds for minimal surfaces arising from min-max constructions
- Iterative q-difference Galois theory
- Conic-connected manifolds
- A visible factor of the special L-value
- Modular Galois covers associated to symplectic resolutions of singularities
- Homeomorphisms in the Sobolev space W1,n–1
