Minimizers of the Willmore functional under fixed conformal class
Differential Geometry
2010-10-01 v1
Abstract
We consider the problem of minimizing the Willmore energy in the class of conformal immersions of a given closed, genus p Riemann surface into R^n for n=3,4. We prove existence of a smooth minimizer, provided that the infimum is below a certain bound . For tori in R^3 we have explicitely .
Keywords
Cite
@article{arxiv.1009.6168,
title = {Minimizers of the Willmore functional under fixed conformal class},
author = {Ernst Kuwert and Reiner Schätzle},
journal= {arXiv preprint arXiv:1009.6168},
year = {2010}
}