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Differential Geometry Seminar
The existence of constrained Willmore surfaces in $\mathbb{R}^3$ and $\mathbb{R}^4$
The existence of constrained Willmore surfaces in $\mathbb{R}^3$ and $\mathbb{R}^4$
Organizers
Speaker
Ross Ogilvie
Time
Tuesday, December 16, 2025 3:00 PM - 4:00 PM
Venue
A7-201
Online
Zoom 388 528 9728
(BIMSA)
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 corresponding "weak" problem, we were able to take limits of sequences of immersions and prove the existence of minimizers in each conformal class.