16 citations · 55 across the 17 of their papers we have counts for
6 papers · 1 filter
Lipschitz extension theorems with explicit constants
Giuliano Basso
In this mostly expository article, we give streamlined proofs of several well-known Lipschitz extension theorems. We pay special attention to obtaining statements with explicit exp…
On a problem of Mazur and Sternbach
Giuliano Basso
We investigate Problem 155 form the "Scottish Book" due to S. Mazur and L. Sternbach. In modern terminology they asked if every bijective, locally isometric map between two real Ba…
Finsler currents
Giuliano Basso
We propose a slight variant of Ambrosio and Kirchheim's definition of a metric current. We show that with this new definition it is possible to obtain certain volume functionals fr…
Integral representation of functions on the circle
Giuliano Basso
We give a complete characterization of all real-valued functions on the unit circle that can be represented by integrating the spherical distance on with respect to a s…
Geometric and analytic structures on metric spaces homeomorphic to a manifold
Giuliano Basso, Denis Marti, Stefan Wenger
We study metric spaces homeomorphic to a closed oriented manifold from both geometric and analytic perspectives. We show that such spaces (which are sometimes called metric manifol…
A non-compact convex hull in generalized non-positive curvature
Giuliano Basso, Yannick Krifka, Elefterios Soultanis
In this article, we are interested in metric spaces that satisfy a weak non-positive curvature condition in the sense that they admit a conical geodesic bicombing. We show that the…