Curvature estimates for surfaces with bounded mean curvature

Theodora Bourni, Giuseppe Tinaglia

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
126 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)5813-5828
Number of pages16
JournalTransactions of the American Mathematical Society
Volume364
Issue number11
DOIs
Publication statusPublished - Nov 2012

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