Curvature bounds on length-minimizing discs

Author:

Alexander Lytchak, Sophia Wagner

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Metric Geometry (math.MG)

journal:

date:

2023-08-27 16:00:00

Abstract

We show that a length-minimizing disk inherites the upper curvature bound of the target. As a consequence we prove that harmonic discs and ruled discs inherit the upper curvature bound from the ambient space.

PDF: Curvature bounds on length-minimizing discs.pdf