The rigidity of embedded constant mean curvature surfaces

2008/01/22 by William H. Meeks III, Meeks, William H., Giuseppe Tinaglia +1
Mathematics · #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A10

paper · pdf · doi:10.48550/arxiv.0801.3409

10 pages

arxiv created 2008/01/22 · arxiv updated 2009/12/01

Abstract

We study the rigidity of complete, embedded constant mean curvature surfaces in R³. Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R³ or its isometry group contains an index two subgroup of isometries that extend.

Related

• The number of constant mean curvature isometric immersions of a surface
• The Moduli Space of Complete Embedded Constant Mean Curvature Surfaces
• The geometry of constant mean curvature surfaces in ℝ³
• Rotationally invariant constant mean curvature surfaces in homogeneous 3-manifolds
• Invariant surfaces in Sol₃ with constant mean curvature and their computer graphics