Constrained Willmore Surfaces

Details Constrained Willmore Surfaces Constrained Willmore Surfaces

2004-11-22

arxiv.org/abs/math/0411479v3

Calc. Var. Partial Differential Equations 32 (2008), 263-277

Mathematics

Differential Geometry

17 pages, 8 figures; v2: Hopf tori added as an example, minor changes in presentation, numbering changed; v3: new abstract and

Scientific paper

10.1007/s00526-007-0142-5

Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $W=\int H^2$ under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the critical points of arbitrary geometric functionals on the space of immersions under the constraint that the admissible variations infinitesimally preserve the conformal structure. Besides constrained Willmore surfaces we discuss in some detail examples of constrained minimal and volume critical surfaces, the critical points of the area and enclosed volume functional under the conformal constraint.

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