Degree Theory of Immersed Hypersurfaces

Details Degree Theory of Immersed Hypersurfaces Degree Theory of Immersed Hypersurfaces

2010-10-09

arxiv.org/abs/1010.1879v2

Mathematics

Differential Geometry

64 pages + ~18 pages appendix. Complete revision of previous version. Stronger results with simpler hypotheses

Scientific paper

We develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function. We apply this theory to count the (algebraic) number of immersed hyperspheres in various cases: where $K$ is mean curvature; extrinsic curvature and special Lagrangian curvature, and we show that in all these cases, this number is equal to $-\chi(M)$, where $\chi(M)$ is the Euler characteristic of $M$.

Affiliated with

Also associated with

No associations

Rating

Degree Theory of Immersed Hypersurfaces 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 Degree Theory of Immersed Hypersurfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Degree Theory of Immersed Hypersurfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-87882