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Date
2013-05-27Type
- Working Paper
ETH Bibliography
yes
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Abstract
We prove that a sequence of possibly branched, weak immersions of the two-sphere S 2 into an arbitrary compact riemannian manifold (M m ,h) with uniformly bounded area and uniformly bounded L 2 − norm of the second fundamental form either collapse to a point or weakly converges as current, modulo extraction of a subsequence, to a Lipschitz mapping of S 2 and whose image is made of a connected union of finitely many, possibly branched, weak immersions of S 2 with finite total curvature. We prove moreover that if the sequence belongs to a class γ of π 2 (M m ) the limiting lipschitz mapping of S 2 realizes this class as well. Show more
Publication status
publishedExternal links
Journal / series
arXivPages / Article No.
Publisher
Cornell UniversityOrganisational unit
03600 - Rivière, Tristan / Rivière, Tristan
Related publications and datasets
Is previous version of: https://doi.org/10.3929/ethz-b-000091454
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ETH Bibliography
yes
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