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Differential Geometry Seminar
The existence of constrained Willmore surfaces in R^3 and R^4.
The existence of constrained Willmore surfaces in R^3 and R^4.
演讲者
Ross Ogilvie
时间
2025年12月16日 15:00 至 16:00
地点
A7-201
线上
Zoom 388 528 9728
(BIMSA)
摘要
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.