Curvature bounds on length-minimizing discs

2023/08/28 by Lytchak, Alexander, Wagner, Sophia
#53C21 #53C23 #53C42 #53C43 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2308.14684

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.

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