A. Savo

activity

20102026

most citedOn the first eigenvalue of the Dirichlet-to-Neumann operator on forms

36 citations · 97 across the 22 of their papers we have counts for

collaborators

26 papers

math.SP2026

Maximisers for the second Neumann eigenvalue of annuli in two-dimensional space forms

Luigi Provenzano, Alessandro Savo

We prove a sharp Szegö-Weinberger-type inequality for balanced doubly connected domains in $S^{2}$ , $R^{2}$ and $H^{2}$ . More precisely, the first positive Neuman…

math.SP2026

Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces

Marco Michetti, Luigi Provenzano, Alessandro Savo

We consider the first eigenvalue of the magnetic Laplacian with zero magnetic field on simply connected compact surfaces and we establish isoperimetric inequalities and upper bound…

math.SP2026

On the isoperimetric inequality for the first positive Neumann eigenvalue on the sphere

Luigi Provenzano, Alessandro Savo

We prove that geodesic disks are the unique maximizers of the first positive Neumann eigenvalue among all simply connected domains in $S^{2}$ with prescribed area. We then sh…

math.DG2025

Rigidity of an overdetermined heat equation and minimal helicoids in space-forms

Andrea Bisterzo, Alessandro Savo

Let $M$ be a Riemannian manifold and $Ω$ a smooth domain of $M$ . We study the following heat diffusion problem: assume that the initial temperature is equal to $1$ , uniformly on $Ω…

math.DG2025

Magnetic ground states and the conformal class of a surface

Bruno Colbois, Luigi Provenzano, Alessandro Savo

On a closed, orientable Riemannian surface $Σ_{g}$ of arbitrary genus $g \geq 1$ and Riemannian metric $h$ we study the magnetic Laplacian with magnetic potential given by a harmonic…

math.SP2024★ 8 cited

A reverse Faber-Krahn inequality for the magnetic Laplacian

Bruno Colbois, Corentin Léna, Luigi Provenzano +1

We consider the first eigenvalue of the magnetic Laplacian in a bounded and simply connected planar domain, with uniform magnetic field and Neumann boundary conditions. We investig…

math.SP2023★ 1 cited

Geometry of the magnetic Steklov problem on Riemannian annuli

Luigi Provenzano, Alessandro Savo

We study the geometry of the first two eigenvalues of a magnetic Steklov problem on an annulus $Σ$ (a compact Riemannian surface with genus zero and two boundary components), the m…

math.SP2023★ 1 cited

Geometric bounds for the magnetic Neumann eigenvalues in the plane

Bruno Colbois, Corentin Léna, Luigi Provenzano +1

We consider the eigenvalues of the magnetic Laplacian on a bounded domain $Ω$ of $R^{2}$ with uniform magnetic field $β > 0$ and magnetic Neumann boundary conditions. We find u…

math.SP2022★ 1 cited

Isoperimetric inequalities for the magnetic Neumann and Steklov problems with Aharonov-Bohm magnetic potential

Bruno Colbois, Luigi Provenzano, Alessandro Savo

We discuss isoperimetric inequalities for the magnetic Laplacian on bounded domains of $R^{2}$ endowed with an Aharonov-Bohm potential. When the flux of the potential around…

math.DG2021

Isoparametric foliations and the Pompeiu problem

Luigi Provenzano, Alessandro Savo

A bounded domain $Ω$ in a Riemannian manifold $M$ is said to have the Pompeiu property if the only continuous function which integrates to zero on $Ω$ and on all its congruent imag…

math.DG2020

On the heat content functional and its critical domains

Alessandro Savo

We study and classify smooth bounded domains in an analytic Riemannian manifold which are critical for the heat content at all times t>0. We do that by first computing the first va…

math.AP2020

Upper bounds for the ground state energy of the Laplacian with zero magnetic field on planar domains

Bruno Colbois, Alessandro Savo

We obtain upper bounds for the first eigenvalue of the magnetic Laplacian associated to a closed potential $1$ -form (hence, with zero magnetic field) acting on complex functions of…

math.SP2020

Lower bounds for the first eigenvalue of the Laplacian with zero magnetic field in planar domains

Bruno Colbois, Alessandro Savo

We study the Laplacian with zero magnetic field acting on complex functions of a planar domain $Ω$ , with magnetic Neumann boundary conditions. If $Ω$ is simply connected then the s…

math.AP2019

Optimal eigenvalue estimates for the Robin Laplacian on Riemannian manifolds

Alessandro Savo

We consider the first eigenvalue $λ_{1} (Ω, σ)$ of the Laplacian with Robin boundary conditions on a compact Riemannian manifold $Ω$ with smooth boundary, $σ \in R$ being the Robin b…

math.DG2018

Index and first Betti number of $f$ -minimal hypersurfaces and self-shrinkers

Debora Impera, Michele Rimoldi, Alessandro Savo

We study the Morse index of self-shrinkers for the mean curvature flow and, more generally, of $f$ -minimal hypersurfaces in a weighted Euclidean space endowed with a convex weight.…

math.SP2017★ 10 cited

The Steklov spectrum of cuboids

Alexandre Girouard, Jean Lagacé, Iosif Polterovich +1

The paper is concerned with the Steklov eigenvalue problem on cuboids of arbitrary dimension. We prove a two-term asymptotic formula for the counting function of Steklov eigenvalue…

math.DG2017

Lower bounds for the first eigenvalue of the magnetic Laplacian

Bruno Colbois, Alessandro Savo

We consider a Riemannian cylinder endowed with a closed potential 1-form A and study the magnetic Laplacian with magnetic Neumann boundary conditions associated with those data. We…

math.DG2017★ 5 cited

Eigenvalue upper bounds for the magnetic Schroedinger operator

Bruno Colbois, Ahmad El Soufi, Said Ilias +1

We study the eigenvalues of the magnetic Schroedinger operator associated with a magnetic potential A and a scalar potential q, on a compact Riemannian manifold M, with Neumann bou…

math.DG2017

Geometric rigidity of constant heat flow

Alessandro Savo

Let $Ω$ be a compact Riemannian manifold with smooth boundary and let $u_{t}$ be the solution of the heat equation on $Ω$ , having constant unit initial data $u_{0} = 1$ and Dirichlet bou…

math.DG2016★ 2 cited

Eigenvalue bounds for the magnetic Laplacian

Bruno Colbois, Alessandro Savo

We consider a compact Riemannian manifold M endowed with a potential 1-form A and study the magnetic Laplacian associated with those data (with Neumann magnetic boundary condition…

math.DG2014

Heat flow, heat content and the isoparametric property

Alessandro Savo

Let $M$ be a Riemannian manifold and $Ω$ a compact domain of $M$ with smooth boundary. We study the solution of the heat equation on $Ω$ having constant unit initial conditions and…

math.MG2013★ 5 cited

Eigenvalues of the Laplacian on a compact manifold with density

Bruno Colbois, Ahmad El Soufi, Alessandro Savo

In this paper, we study the spectrum of the weighted Laplacian (also called Bakry-Emery or Witten Laplacian) $L_{σ}$ on a compact, connected, smooth Riemannian manifold $(M, g)$ endow…

math.DG2012

Sharp bounds for the first eigenvalue of a fourth order Steklov problem

Simon Raulot, Alessandro Savo

We study the biharmonic Steklov eigenvalue problem on a compact Riemannian manifold $Ω$ with smooth boundary. We give a computable, sharp lower bound of the first eigenvalue of thi…

math.DG2012

On the spectrum of the Dirichlet-to-Neumann operator acting on forms of a Euclidean domain

Simon Raulot, Alessandro Savo

We compute the whole spectrum of the Dirichlet-to-Neumann operator acting on differential p-forms on the unit Euclidean ball. Then, we prove a new upper bound for its first eigenva…

Maximisers for the second Neumann eigenvalue of annuli in two-dimensional space forms

Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces

On the isoperimetric inequality for the first positive Neumann eigenvalue on the sphere

Rigidity of an overdetermined heat equation and minimal helicoids in space-forms

Magnetic ground states and the conformal class of a surface

A reverse Faber-Krahn inequality for the magnetic Laplacian

Geometry of the magnetic Steklov problem on Riemannian annuli

Geometric bounds for the magnetic Neumann eigenvalues in the plane

Isoperimetric inequalities for the magnetic Neumann and Steklov problems with Aharonov-Bohm magnetic potential

Isoparametric foliations and the Pompeiu problem

On the heat content functional and its critical domains

Upper bounds for the ground state energy of the Laplacian with zero magnetic field on planar domains

Lower bounds for the first eigenvalue of the Laplacian with zero magnetic field in planar domains

Optimal eigenvalue estimates for the Robin Laplacian on Riemannian manifolds

Index and first Betti number of f-minimal hypersurfaces and self-shrinkers

The Steklov spectrum of cuboids

Lower bounds for the first eigenvalue of the magnetic Laplacian

Eigenvalue upper bounds for the magnetic Schroedinger operator

Geometric rigidity of constant heat flow

Eigenvalue bounds for the magnetic Laplacian

Heat flow, heat content and the isoparametric property

Eigenvalues of the Laplacian on a compact manifold with density

Sharp bounds for the first eigenvalue of a fourth order Steklov problem

On the spectrum of the Dirichlet-to-Neumann operator acting on forms of a Euclidean domain

Index and first Betti number of $f$ -minimal hypersurfaces and self-shrinkers