Concentration of small Willmore spheres in Riemannian 3-manifolds
METADATA ONLY
Loading...
Author / Producer
Date
2013-10-26
Publication Type
Working Paper
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
Abstract
Given a 3-dimensional Riemannian manifold (M,g) , we prove that if (Φ k ) is a sequence of Willmore spheres (or more generally area-constrained Willmore spheres), having Willmore energy bounded above uniformly strictly by 8π , and Hausdorff converging to a point p ¯ ∈M , then Scal(p ¯ )=0 and ∇Scal(p ¯ )=0 (resp. ∇Scal(p ¯ )=0 ). Moreover, a suitably rescaled sequence smoothly converges, up to subsequences and reparametrizations, to a round sphere in the euclidean 3-dimensional space. This generalizes previous results of Lamm and Metzger contained in \cite{LM1}-\cite{LM2}. An application to the Hawking mass is also established.
Permanent link
Publication status
published
External links
Editor
Book title
Journal / series
Volume
Pages / Article No.
Publisher
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Organisational unit
03600 - Rivière, Tristan / Rivière, Tristan
Notes
Submitted on 26 October 2013.