Stability of Helicoids in Hyperbolic Three-Dimensional Space
classification
🧮 math.DG
math.GT
keywords
minimalhelicoidshyperbolicspacesurfaceconstantexistsfamily
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For a family of minimal helicoids H_a in the hyperbolic 3-space, there exists a constant a_c=2.17966 such that the following statements are true: (1) H_a is a globally stable minimal surface if 0<=a<=a_c, and (2) H_a is an unstable minimal surface with index one if a>a_c.
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