How to construct metrics to control distributions of homologically mass-minimizing currents

2015/01/08 by Yongsheng Zhang, Zhang, Yongsheng · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1501.01836

20 pages, 6 figures. Comments are welcome

arxiv created 2015/01/08 · arxiv updated 2015/01/09

Abstract

By Federer and Fleming there exist at least one mass-minimizing normal current in every real-valued homology class of a Riemannian manifold. However the regularity of the mass-minimizing currents and their distributions may generally be quite complicated. In this paper we shall study how to construct nice metrics so that (as functionals over smooth forms) almost all homologically mass-minimizing currents are just linear combinations over smooth submanifolds.

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