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math.DG2025
Hilbert space factor of metric spaces
Thomas Foertsch, Alexander Lytchak, Elefterios Soultanis
We prove that any complete metric space has a unique decomposition as a direct product of a possibly finite or zero-dimensional Hilbert space and a space that does not split off li…
math.DG2024
Smoothness of submetries
Alexander Lytchak, Burkhard Wilking
We prove that a Riemannian submersion between smooth, compact, non-negatively curved Riemannian manifolds has to be smooth, resolving a conjecture by Berestovskii--Guijarro. We sho…