A Remark on the Non-Compactness of W^2,d Immersions of d-Dimensional Hypersurfaces release_3yc62aaewvbtveuhkueizcakga

by Siran Li

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We consider the continuous W^2,d immersions of d-dimensional hypersurfaces in R^d+1 with second fundamental forms uniformly bounded in L^d. Two results are obtained: first, a family of such immersions is constructed, whose limit fails to be an immersion of a manifold. This addresses the endpoint cases in J. Langer and P. Breuning. Second, under the additional assumption that the Gauss map is slowly oscillating, we prove that any family of such immersions subsequentially converges to a set locally parametrised by Hölder functions.
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Type  paper-conference
Stage   submitted
Date   2019-06-09
Version   v2
Language   en ?
arXiv  1807.00360v2
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