arXiv subjects

P. Ursino

Publications and source records attributed to P. Ursino.

3 recordsLinked to original sources

arXiv2023

Volume of Tubes and Concentration of Measure in Riemannian Geometry

We investigate the notion of concentration locus introduced in \cite{CacUrs22}, in the case of Riemann manifolds sequences and its relationship with the volume of tubes. After providing a general formula for the volume of a tube around a Riemannian submanifold of a Riemannian manifold, we specialize it to the case of totally geodesic submanifolds of compact symmetric spaces. In the case of codimension one, we prove explicitly concentration. Then, we investigate for possible characterizations of concentration loci in terms of Wasserstein and Box distances.

math.DG↗

arXiv2022

Concentration of measure for classical Lie groups

We study concentration of measure in Lie group actions. We define the notion of concentration locus of a flag sequence of Lie groups. Some examples of infinite group action on an infinite dimensional compact and non compact manifold show the role played by the trajectory of concentration locus. We also provide some applications in Physics, which emphasize the role of concentration of measure in gravitational effects.

math.GR↗

arXiv2001

Embeddings into P(N)/fin and extension of automorphisms

Given a Boolean algebra B and an embedding e:B -> P(N)/fin we consider the possibility of extending each or some automorphism of B to the whole P(N)/fin. Among other things, we show, assuming CH, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.

math.LO↗