Smyth, Brian ; Tinaglia, Giuseppe
(2008)
The isometric deformability question for constant mean curvature surfaces with topology.
[Preprint]
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Abstract
The paper treats the isometric deformability of non-simply-connected constant mean curvature surfaces which are neither assumed embedded nor complete. We prove that if a smooth oriented surface M immersed in R^3 admits a nontrivial isometric deformation with constant mean curvature H then every cycle in M has vanishing flux and, when H is not zero, also vanishing torque. The vanishing of all fluxes implies the existence of such an isometric deformation when H = 0. Our work generalizes to constant mean curvature surfaces a well-known rigidity result for minimal surfaces.
Abstract
The paper treats the isometric deformability of non-simply-connected constant mean curvature surfaces which are neither assumed embedded nor complete. We prove that if a smooth oriented surface M immersed in R^3 admits a nontrivial isometric deformation with constant mean curvature H then every cycle in M has vanishing flux and, when H is not zero, also vanishing torque. The vanishing of all fluxes implies the existence of such an isometric deformation when H = 0. Our work generalizes to constant mean curvature surfaces a well-known rigidity result for minimal surfaces.
Document type
Preprint
Creators
Subjects
DOI
Deposit date
31 Mar 2008
Last modified
16 May 2011 12:08
URI
Other metadata
Document type
Preprint
Creators
Subjects
DOI
Deposit date
31 Mar 2008
Last modified
16 May 2011 12:08
URI
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