Least area Spherical Catenoids in Hyperbolic Three-Dimensional Space

2012/04/22 by Biao Wang, Wang, Biao · 2 citations
Mathematics · #53A10 (Primary) #53C42 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #math.GT #msc:53A10 #msc:53C42

paper · pdf · doi:10.48550/arxiv.1204.4943

25 pages, 12 figures

openalex publication_date 2012/04/22 · arxiv created 2015/02/17 · arxiv updated 2015/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a family of spherical minimal catenoids C_a in the hyperbolic 3-space, there exist two constants 0<a_c<a_l such that the following are true: (1) C_a is an unstable minimal surface with index one if a<a_c, (2) C_a is a stable minimal surface if a>=a_c, and (3) C_a is a least area minimal surface in the sense of Meeks-Yau if a>=a_l.

Cited by

• Counting Minimal Surfaces in Quasi-Fuchsian three-Manifolds
• Stability of Catenoids and Helicoids in Hyperbolic Space

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