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Licensed Unlicensed Requires Authentication Published by De Gruyter January 3, 2013

Lipschitz conformal immersions from degenerating Riemann surfaces with L2-bounded second fundamental forms

Tristan Rivière

Abstract.

We give an asymptotic lower bound for the Willmore energy of weak immersions with degenerating conformal class. This lower bound is used in several other works. It is for instance one of the ingredients used by the author (2010) for providing an alternative proof of the one by L. Simon of the existence of a smooth torus minimizing the Willmore energy. The main result of the present paper has been independently obtained by Kuwert and Li (2010).

Received: 2011-06-17
Revised: 2011-11-02
Accepted: 2011-11-08
Published Online: 2013-01-03
Published in Print: 2013-01-01

© 2013 by Walter de Gruyter Berlin Boston