Curvature estimates for submanifolds with prescribed Gauss image and mean curvature

Details Curvature estimates for submanifolds with prescribed Gauss image and mean curvature Curvature estimates for submanifolds with prescribed Gauss image and mean curvature

2008-12-19

arxiv.org/abs/0812.3710v1

Mathematics

Differential Geometry

Scientific paper

We study that the $n-$graphs defining by smooth map $f:\Om\subset \ir{n}\to \ir{m}, m\ge 2,$ in $\ir{m+n}$ of the prescribed mean curvature and the Gauss image. We derive the interior curvature estimates $$\sup_{D_R(x)}|B|^2\le\f{C}{R^2}$$ under the dimension limitations and the Gauss image restrictions. If there is no dimension limitation we obtain $$\sup_{D_R(x)}|B|^2\le C R^{-a}\sup_{D_{2R}(x)}(2-\De_f)^{-(\f{3}{2}+\f{1}{s})}, \qquad s=\min(m, n)$$ with $a<1$ under the condition $$\De_f=[\text{det}(\de_{ij}+\sum_\a\pd{f^\a}{x^i}\pd{f^\a}{x^j})]^{\f{1}{2}}<2.$$ If the image under the Gauss map is contained in a geodesic ball of the radius $\f{\sqrt{2}}{4}\pi$ in $\grs{n}{m}$ we also derive corresponding estimates.

Affiliated with

Also associated with

No associations

Rating

Curvature estimates for submanifolds with prescribed Gauss image and 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 submanifolds with prescribed Gauss image and mean curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Curvature estimates for submanifolds with prescribed Gauss image and mean curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-726821