Luca Benatti

works on

curve networks 1 geometric flows 1 gradient flow 1 higher-order PDE 1 long-time existence 1

From the 1 of 5 linked papers with an AI index.

collaborators

5 papers

math.AP2026

One thousand and one higher-order geometric flows of networks

Luca Benatti, Alessandra Pluda

The paper proves short-time existence and uniqueness (up to reparametrization) for many higher-order geometric flows of curves and networks derived as L²‑gradient flows of curvatur…

math.DG2026

Nonlinear potential theory and Ricci-pinched 3-manifolds

Luca Benatti, Ariadna LeÃ³n QuirÃ³s, 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.DG2026

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.DG2026

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…

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…