Genus bounds for min-max minimal surfaces
نویسندگان
چکیده
منابع مشابه
Genus Bounds for Minimal Surfaces Arising from Min-max Constructions
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 Rubistein 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...
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In this paper we survey with complete proofs some well–known, but hard to find, results about constructing closed embedded minimal surfaces in a closed 3-dimensional manifold via min–max arguments. This includes results of J. Pitts, F. Smith, and L. Simon and F. Smith. The basic idea of constructing minimal surfaces via min–max arguments and sweep-outs goes back to Birkhoff, who used such a met...
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Even though the classification of genus zero, embedded minimal surfaces is not complete, W. H. Meeks J. Perez and A. Ros [14], [15], [16] have made progress concerning the question of the uniqueness of the Riemann examples in the class of genus zero embedded minimal surfaces which have an infinite number of ends. They conjecture in [15] that every embedded minimal surface of finite genus and wi...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2019
ISSN: 0022-040X
DOI: 10.4310/jdg/1563242473