Two-dimensional metric spaces with curvature bounded above I

Abstract

We determine the local geometric structure of two-dimensional metric spaces with curvature bounded above as the union of finitely many properly embedded/branched immersed Lipschitz disks. As a result, we obtain a graph structure of the topological singular point set of such a singular surface.

73 pages, 12figures, Theorem 1.5 was removed, and the proof of Lemma 7.16 was modified

References in corpus (1)

• Metric minimizing surfaces revisited