Lower Semi-continuity of the Index in the Viscosity Method for Minimal Surfaces
OPEN ACCESS
Loading...
Author / Producer
Date
2021-04
Publication Type
Journal Article
ETH Bibliography
yes
OPEN ACCESS
Data
Rights / License
Abstract
The goal of the present work is two-fold. First we prove the existence of a Hilbert manifold structure on the space of immersed oriented closed surfaces with three derivatives in L2 in an arbitrary compact submanifold Mm of an Euclidian space RQ. Second, using this Hilbert manifold structure, we prove a lower semi-continuity property of the index for sequences of conformal immersions, critical points to the viscous approximation of the area satisfying a Struwe entropy estimate and a bubble tree strongly converging in W1,2 to a limiting minimal surface as the viscous parameter is going to zero.
Permanent link
Publication status
published
External links
Editor
Book title
Journal / series
Volume
2021 (8)
Pages / Article No.
5651 - 5675
Publisher
Oxford University Press
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Organisational unit
03600 - Rivière, Tristan / Rivière, Tristan
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.