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  Curvature estimates for surfaces with bounded mean curvature

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.

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1007.3425 (Preprint), 162KB
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 Creators:
Bourni, Theodora1, Author           
Tinaglia, Giuseppe, Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24012              

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Free keywords: Mathematics, Differential Geometry, math.DG, MSC 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
 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.

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 Dates: 2010-07-202012
 Publication Status: Issued
 Pages: 17 pages, no figures, submitted
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 1007.3425
URI: http://arxiv.org/abs/1007.3425
 Degree: -

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Title: Transactions of the American Mathematical Society
Source Genre: Journal
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Pages: - Volume / Issue: 364 (11 ) Sequence Number: - Start / End Page: 5813 - 5828 Identifier: -