SMS scnews item created by Catherine Meister at Mon 4 Aug 2025 0927
Type: Seminar
Distribution: World
Expiry: 18 Aug 2025
Calendar1: 6 Aug 2025 1300-1400
CalLoc1: SMRI Seminar Room (Macleay Building A12 Room 301)
CalTitle1: The existence of constrained Willmore surfaces in R^3 and R^4
Auth: cmeister@10.48.25.164 (cmei0631) in SMS-SAML

Geometry and Topology Seminar: Ogilvie

The existence of constrained Willmore surfaces in R^3 and R^4



Speaker: Ross Ogilvie, University of Mannheim

Abstract: The Willmore energy of a immersion of a closed surface is the integral of the square of its mean curvature. This is a measure of how far a surface is from being a sphere. It is a conformal invariant. A constrained Willmore surface is a critical point of this energy functional under deformations that preserve the conformal class of the surface. By describing a surface in terms of "holomorphic" data, the Kodaira and Weierstrass representations, and formulating a a corresponding "weak" problem, we were able to take limits of sequences of immersions and prove the existence of minimizers in each conformal class.

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