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arXiv · 1007.3425

Curvature estimates for surfaces with bounded mean curvature

Theodora Bourni·Giuseppe Tinaglia
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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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Theodora Bourni, Giuseppe Tinaglia. 2010-07-20. Curvature estimates for surfaces with bounded mean curvature. https://arxiv.org/abs/1007.3425

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