Luca Benatti

collaborators

4 papers

math.DG2025

The equivalence of isocapacitary notions of mass

Luca Benatti

In this short note, we will prove the equivalence of the isocapacitary notions of mass. This family also includes G. Huisken's isoperimetric mass and J. L. Jauregui's isocapacitary…

math.DG2024

Nonlinear potential theory and Ricci-pinched 3-manifolds

Luca Benatti, Ariadna León Quirós, Francesca Oronzio +1

In this paper, we focus on Hamilton's pinching conjecture formulated in Hamilton's paper "Three-manifolds with positive Ricci curvature". Let $(M, g)$ be a complete, connected, non…

math.DG2024

Fine properties of nonlinear potentials and a unified perspective on monotonicity formulas

Luca Benatti, Alessandra Pluda, Marco Pozzetta

We rigorously show that a large family of monotone quantities along the weak inverse mean curvature flow is the limit case of the corresponding ones along the level sets of $p$ -cap…

math.DG2024

A Note on Ricci-pinched three-manifolds

Luca Benatti, Carlo Mantegazza, Francesca Oronzio +1

Let $(M, g)$ be a complete, connected, non-compact Riemannian $3$ -manifold. Suppose that $(M, g)$ satisfies the Ricci--pinching condition $Ric \geq ε R g$ f…