English

Constrained Willmore Surfaces

Differential Geometry 2009-09-29 v3

Abstract

Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy W=H2W=\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.

Keywords

Cite

@article{arxiv.math/0411479,
  title  = {Constrained Willmore Surfaces},
  author = {Christoph Bohle and G. Paul Peters and Ulrich Pinkall},
  journal= {arXiv preprint arXiv:math/0411479},
  year   = {2009}
}

Comments

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