Hierarchy structures in finite index CMC surfaces

Author:

Meeks III William H.1,Pérez Joaquín2ORCID

Affiliation:

1. Mathematics Department , University of Massachusetts , Amherst , MA 01003 , USA

2. Department of Geometry and Topology and Institute of Mathematics (IMAG) , University of Granada , 18071 Granada , Spain

Abstract

Abstract Given ε 0 > 0 {{\varepsilon}_{0}>0} , I { 0 } {I\in\mathbb{N}\cup\{0\}} and K 0 , H 0 0 {K_{0},H_{0}\geq 0} , let X be a complete Riemannian 3-manifold with injectivity radius Inj ( X ) ε 0 {\operatorname{Inj}(X)\geq{\varepsilon}_{0}} and with the supremum of absolute sectional curvature at most K 0 {K_{0}} , and let M X {M\looparrowright X} be a complete immersed surface of constant mean curvature H [ 0 , H 0 ] {H\in[0,H_{0}]} with index at most I. For such M X {M\looparrowright X} , we prove a structure theorem which describes how the interesting ambient geometry of the immersion is organized locally around at most I points of M, where the norm of the second fundamental form takes on large local maximum values.

Funder

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Agencia Estatal de Investigación

Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Geometry of branched minimal surfaces of finite index;Advanced Nonlinear Studies;2024-02-01

2. Geometry of CMC surfaces of finite index;Advanced Nonlinear Studies;2023-01-01

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