On the Dimension of the Singular Set of Perimeter Minimizers in Spaces with a Two-Sided Bound on the Ricci Curvature

Abstract

Listen

Translate article

We show that the Hausdorff dimension of the singular set of perimeter minimizers in noncollapsed limits of manifolds with two-sided bounds on the Ricci curvature is at most n-5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n-5$$\\end{document}, where n is the dimension of the ambient space. The estimate is sharp.