TITLE

Constrained Willmore surfaces

AUTHOR(S)
Bohle, Christoph; Peters, G. Paul; Pinkall, Ulrich
PUB. DATE
June 2008
SOURCE
Calculus of Variations & Partial Differential Equations;Jun2008, Vol. 32 Issue 2, p263
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $${\mathcal{W}} = \int H^2$$ 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.
ACCESSION #
31342434

 

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