Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in R^n

Details Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in R^n Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in R^n

2004-04-27

arxiv.org/abs/math/0404481v1

Mathematics

Metric Geometry

Scientific paper

In (the surface of) a convex polytope P^3 in R^4, an area-minimizing surface avoids the vertices of P and crosses the edges orthogonally. In a smooth Riemannian manifold M with a group of isometries G, an area-minimizing G-invariant oriented hypersurface is smooth (except for a very small singular set in high dimensions). Already in 3D, area-minimizing G-invariant unoriented surfaces can have certain singularities, such as three orthogonal sheets meeting at a point. We also treat other categories of surfaces such as rectifiable currents modulo nu and soap films.

Affiliated with

Also associated with

No associations

Rating

Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in R^n 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 Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in R^n, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in R^n will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-511243