33 citations · 96 across the 16 of their papers we have counts for
16 papers
Estimates for the p-Green function near the pole
Stefano Borghini, Virginia Agostiniani
We study the asymptotic expansion of p-Green functions and their derivatives near the pole. In the Euclidean setting, we strengthen a theorem from [arXiv:2203.01206] by establishin…
Mass-type invariants in the presence of a cosmological constant
Virginia Agostiniani, Stefano Borghini, Lorenzo Mazzieri
In this paper, we introduce a new family of mass-type invariants for time-symmetric initial data in space-times satisfying the Dominant Energy Condition. For positive cosmological…
On the Serrin problem for ring-shaped domains: the -dimensional case
Virginia Agostiniani, Chiara Bernardini, Stefano Borghini +1
We provide several characterizations of ring-shaped rotationally symmetric solutions to the Serrin problem in arbitrary dimensions.
Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes
Stefano Borghini, Carla Cederbaum, Albachiara Cogo
We study 4-dimensional asymptotically flat electrostatic electro-vacuum spacetimes with a connected black hole, photon sphere, or equipotential photon surface inner boundary. Our a…
Comparison geometry for substatic manifolds and a weighted Isoperimetric Inequality
Stefano Borghini, Mattia Fogagnolo
Substatic Riemannian manifolds with minimal boundary arise naturally in General Relativity as spatial slices of static spacetimes satisfying the Null Energy Condition. Moreover, th…
The equality case in the substatic Heintze-Karcher inequality
Stefano Borghini, Mattia Fogagnolo, Andrea Pinamonti
We provide a rigidity statement for the equality case for the Heintze-Karcher inequality in substatic manifolds. We apply such result in the warped product setting to fully remove…
Counterexamples to a divergence lower bound for the covariant derivative of skew-symmetric 2-tensor fields
Stefano Borghini, Lorenzo Mazzieri
In arXiv:2103.15482 an estimate for suitable skew-symmetric 2-tensors was claimed. Soon after, this estimate has been exploited to claim powerful classification results: most notab…
Symmetry results for Serrin-type problems in doubly connected domains
Stefano Borghini
In this work, we employ the technique developed in arXiv:2109.11255 to prove rotational symmetry for a class of Serrin-type problems for the standard laplacian. We also discuss in…
On the Serrin problem for ring-shaped domains
Virginia Agostiniani, Stefano Borghini, Lorenzo Mazzieri
In this paper, we deal with the long standing open problem of characterising rotationally symmetric solutions to , when Dirichlet boundary conditions are imposed on a ring…
Static Black Hole Uniqueness for nonpositive masses
Stefano Borghini
In arXiv:1310.3002, Lee and Neves proved a Penrose inequality for spacetimes with negative cosmological constant and nonpositive mass aspect. As an application, they were able to o…
On the uniqueness of Schwarzschild-de Sitter spacetime
Stefano Borghini, Piotr T. Chruściel, Lorenzo Mazzieri
We establish a new uniqueness theorem for the three dimensional Schwarzschild-de Sitter metrics. For this some new or improved tools are developed. These include a reverse Lojasiew…
On the mass of static metrics with positive cosmological constant -- II
Stefano Borghini, Lorenzo Mazzieri
This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and…
On the mass of static metrics with positive cosmological constant - I
Stefano Borghini, Lorenzo Mazzieri
In this paper we propose and discuss a notion of mass for compact static metrics with positive cosmological constant. As a consequence, we characterise the de Sitter solution as th…
Some Sphere Theorems in Linear Potential Theory
Stefano Borghini, Giovanni Mascellani, Lorenzo Mazzieri
In this paper we analyze the capacitary potential due to a charged body in order to deduce sharp analytic and geometric inequalities, whose equality cases are saturated by domains…
Monotonicity formulas for static metrics with non-zero cosmological constant
Stefano Borghini, Lorenzo Mazzieri
In this paper we study non-singular vacuum static space-times with non-zero cosmological constant. We introduce new integral quantities, and under suitable assumptions we prove the…
A gluing formula for Reidemeister-Turaev torsion
Stefano Borghini
We extend Turaev's theory of Euler structures and torsion invariants on 3-manifolds to the case of vector fields having generic behavior on the boundary. This allows to easily defi…