Constrained Willmore surfaces |
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Authors: | Christoph Bohle G Paul Peters Ulrich Pinkall |
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Institution: | 1.Institut für Mathematik,Technische Universit?t Berlin,Berlin,Germany |
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Abstract: | Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy
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.
C. Bohle, G. P. Peters and U. Pinkall are partially supported by DFG SPP 1154. |
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Keywords: | 53C42 53A30 53A05 |
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