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math.DG2023
Curvature bounds on length-minimizing discs
Alexander Lytchak, Sophia Wagner
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 b…
math.DG2023
Some Regularity of submetries
Alexander Lytchak
We discuss regularity statements for equidistant decompositions of Riemannian manifolds and for the corresponding quotient spaces. We show that any stratum of the quotient space ha…
math.MG2023
A note on subsets of positive reach
Alexander Lytchak
We provide new structural results on sets of positive reach in Euclidean spaces and Riemannian manifolds.