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Journal Article

Curvature estimates for surfaces with bounded mean curvature

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons4409

Bourni,  Theodora
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1007.3425
(Preprint), 162KB

1007.3425v3.pdf
(Preprint), 170KB

TransAMS-2012-05487-0.pdf
(Any fulltext), 243KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Bourni, T., & Tinaglia, G. (2012). Curvature estimates for surfaces with bounded mean curvature. Transactions of the American Mathematical Society, 364(11 ), 5813-5828. Retrieved from http://arxiv.org/abs/1007.3425.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-C6CB-F
Abstract
Estimates for the norm of the second fundamental form, $|A|$, play a crucial role in studying the geometry of surfaces. In fact, when $|A|$ is bounded the surface cannot bend too sharply. In this paper we prove that for an embedded geodesic disk with bounded $L^2$ norm of $|A|$, $|A|$ is bounded at interior points, provided that the $W^{1,p}$ norm of its mean curvature is sufficiently small, $p>2$. In doing this we generalize some renowned estimates on $|A|$ for minimal surfaces.