16 citations · 55 across the 17 of their papers we have counts for
17 papers
Erratum to "Computation of maximal projection constants"
Giuliano Basso
This is an erratum to the article: "Computation of maximal projection constants" (J. Funct. Anal., 277). The statement of Lemma 3.1(2) of that paper is incorrect. As a consequence…
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…
Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces
Giuliano Basso, Paul Creutz, Elefterios Soultanis
In this paper we consider metric fillings of convex bodies. We show that convex bodies are the unique minimal fillings of their boundary metrics among all i…
Undistorted fillings in subsets of metric spaces
Giuliano Basso, Stefan Wenger, Robert Young
We prove that if a quasiconvex subset of a metric space has finite Nagata dimension and is Lipschitz -connected or admits Euclidean isoperimetric inequalities up to dime…
Absolute Lipschitz extendability and linear projection constants
Giuliano Basso
We prove that the absolute extendability constant of a finite metric space may be determined by computing relative projection constants of certain Lipschitz-free spaces. As an appl…
Approximating spaces of Nagata dimension zero by weighted trees
Giuliano Basso, Hubert Sidler
We prove that if a metric space has Nagata dimension zero with constant , then there exists a dense subset of that is -bilipschitz equivalent to a weighted tree. The…
Extending and improving conical bicombings
Giuliano Basso
We study metric spaces that admit a conical bicombing and thus obey a weak form of non-positive curvature. Prime examples of such spaces are injective metric spaces. In this articl…
Almost minimal orthogonal projections
Giuliano Basso
The projection constant of a finite-dimensional Banach space is by definition the smallest norm of a linear projection of $\ell_\inf…
Computation of maximal projection constants
Giuliano Basso
The linear projection constant of a finite-dimensional real Banach space is the smallest number such that is a -absolute retract in the categor…
Lipschitz extensions to finitely many points
Giuliano Basso
We consider Lipschitz maps with values in quasi-metric spaces and extend such maps to finitely many points. We prove that in this context every 1-Lipschitz map admits an extension…
Conical geodesic bicombings on subsets of normed vector spaces
Giuliano Basso, Benjamin Miesch
We prove existence and uniqueness results for conical geodesic bicombings on subsets of normed vector spaces. Concerning existence, we give a first example of a non-consistent conv…
Fixed point theorems for metric spaces with a conical geodesic bicombing
Giuliano Basso
We derive two fixed point theorems for a class of metric spaces that includes all Banach spaces and all complete Busemann spaces. We obtain our results by the use of a 1-Lipschitz…