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Canal Classes and Cheeger Sets
Nico Lombardi, Christian Richter, Eugenia Saorín Gómez
Giannopoulos, Hartzoulaki and Paouris asked in \cite{GHP} whether the best ratio between volume and surface area of convex bodies sharing a given orthogonal projection onto a fixed…
Translation invariant valuations on quasi-concave functions
Andrea Colesanti, Nico Lombardi, Lukas Parapatits
We study real-valued, continuous and translation invariant valuations defined on the space of quasi-concave functions of N variables. In particular, we prove a homogeneous decompos…
Valuations on the space of quasi-concave functions
Andrea Colesanti, Nico Lombardi
We characterize the valuations on the space of quasi-concave functions defined on the -dimensional Euclidean space, that are rigid motion invariant and continuous with respect t…