Curvature estimates for surfaces with bounded mean curvature

Details Curvature estimates for surfaces with bounded mean curvature Curvature estimates for surfaces with bounded mean curvature

2010-07-20

arxiv.org/abs/1007.3425v3

Mathematics

Differential Geometry

17 pages, no figures, submitted

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Curvature estimates for surfaces with bounded mean curvature does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Curvature estimates for surfaces with bounded mean curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Curvature estimates for surfaces with bounded mean curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-125950