Stability of Helicoids in Hyperbolic Three-Dimensional Space

2015/02/17 by Wang, Biao
#53A10 (Primary) #53C42 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1502.04764

Abstract

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.

Related

• Stability of Catenoids and Helicoids in Hyperbolic Space
• Helicoidal minimal surfaces of prescribed genus, II
• Least area Spherical Catenoids in Hyperbolic Three-Dimensional Space
• Non-proper helicoid-like limits of closed minimal surfaces in 3-manifolds
• Stable minimal hypersurfaces in the hyperbolic space