Curvature estimates for surfaces with bounded mean curvature

Bourni, Theodora; Tinaglia, Giuseppe

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Curvature estimates for surfaces with bounded mean curvature

MPS-Authors

/persons/resource/persons4409

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

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

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: https://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.