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math.DG2026
Orientability of metric manifolds and metric spaces with curvature bounds
Nicola Cavallucci, Denis Marti, Andrea Mondino +1
We develop a theory of orientability for metric manifolds and singular metric spaces using locally integral currents. For topological -manifolds with locally finite Hausdorff me…
math.DG2026
Sobolev-to-Lipschitz property of geodesically complete spaces with curvature bounded from above
Emanuele Caputo, Nicola Cavallucci, Toni Ikonen
We prove that every length space with curvature bounded from above that is geodesically complete has the Sobolev-to-Lipschitz property with exponent infinity. That is, every Sobole…
math.DG2023
The Metric Completion of the Space of Vector-Valued One-Forms
Nicola Cavallucci, Zhe Su
The space of full-ranked one-forms on a smooth, orientable, compact manifold (possibly with boundary) is metrically incomplete with respect to the induced geodesic distance of the…