Regularity of volume-minimizing flows on 3-manifolds

Details Regularity of volume-minimizing flows on 3-manifolds Regularity of volume-minimizing flows on 3-manifolds

2005-05-12

arxiv.org/abs/math/0505263v1

Mathematics

Differential Geometry

11 pages, no figures, LaTeX

Scientific paper

In this article, we show that, for any compact 3-manifold, there is a $C^{1}$ volume-minimizing one-dimensional foliation. More generally, we show the existence of mass-minimizing rectifiable sections of sphere bundles without isolated "pole points" in the base manifold. This same analysis is used to show that the examples, due to Sharon Pedersen, of potentially volume-minimizing rectifiable sections (rectifiable foliations) of the unit tangent bundle to $S^{2n+1}$ are not, in fact, volume minimizing.

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