8 citations · 11 across the 7 of their papers we have counts for
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Minimal tubes of the sphere as the dimension grows: Volume and explosion of the mean exit time
Vicent Gimeno i Garcia, Martín Torres-Valverde
The mean exit time of a Brownian motion from a tube around a closed, minimal embedded \(n\)-dimen\-sional submanifold of the \((n+m)\)-dimen\-sional sphere is studied, establishing…
Measure Concentration around Minimal Hypersurfaces
Vicent Gimeno i Garcia, Vicente Palmer
The classical measure concentration phenomenon on the standard sphere asserts that the volume of any tubular neighborhood of a totally geodesic equator $\mathbb{S}^{…
Dirichlet--Neumann duality for the Basic Spectrum of Riemannian Submersions: A Supersymmetric Perspective
Vicent Gimeno i Garcia, Paulo Henryque da Costa Silva
This manuscript investigates the spectral geometry of Riemannian submersions whose fibers have a basic mean curvature. By restricting the Laplace--Beltrami operator to the space of…
Criteria for parabolicity and hyperbolicity of conductive Riemannian manifolds
Vicent Gimeno i Garcia, Ana Hurtado, Steen Markvorsen +1
Motivated by the physics of anisotropic conductive materials we consider a linear elliptic operator of divergence type on a Riemannian manifold . The…
Evolution of the Torsional Rigidity under Geometric Flows
Vicent Gimeno i Garcia, Fernán González-Ibáñez
This paper explores the behavior of the torsional rigidity of a precompact domain as the ambient manifold evolves under a geometric flow. Specifically, we derive bounds on torsiona…
Fat equator effect and Minimality in immersions and submersions of the Sphere
Vicent Gimeno i Garcia, Vicente Palmer
Inspired by the equatorial concentration of measure phenomenon in the sphere, a result which is deduced from the general, (and intrinsic), concentration of measure in $\mathbb{S}^n…
Parabolicity of invariant Surfaces
Andrea Del Prete, Vicent Gimeno i Garcia
We present a clear and practical way to characterize the parabolicity of a complete immersed surface that is invariant with respect to a Killing vector field of the ambient space.