- Working Paper
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
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Organisational unit03600 - Rivière, Tristan
NotesSubmitted on 27 May 2013.
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