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$ C^1$-regularity for local graph representations of immersions

Author: Patrick Breuning
Journal: Trans. Amer. Math. Soc. 365 (2013), 6185-6198
MSC (2010): Primary 53C42, 53B25
Published electronically: July 10, 2013
MathSciNet review: 3105747
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Abstract: We consider immersions admitting uniform graph representations over the affine tangent space over a ball of fixed radius $ r>0$. We show that for sufficiently small $ C^0$-norm of the graph functions, each graph function is smooth with small $ C^1$-norm.

References [Enhancements On Off] (What's this?)

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  • 4. S. Delladio: On Hypersurfaces in $ \mathrm {R}^{n+1}$ with Integral Bounds on Curvature, J. Geom. Anal., 11: 17-41, 2000. MR 1829346 (2002a:49059)
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Additional Information

Patrick Breuning
Affiliation: Institut für Mathematik der Goethe Universität Frankfurt am Main, Robert-Mayer-Straße 10, D-60325 Frankfurt am Main, Germany
Address at time of publication: Fakultät für Mathematik des Karlsruhe Institute of Technology, Institut für Analysis, Kaiserstrasse 89-93, D-76133 Karlsruhe, Germany

Received by editor(s): July 30, 2011
Published electronically: July 10, 2013
Additional Notes: This work was supported by the DFG-Forschergruppe Nonlinear Partial Differential Equations: Theoretical and Numerical Analysis. The contents of this paper were part of the author’s dissertation, which was written at Universität Freiburg, Germany
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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