From the 1 of 5 linked papers with an AI index.
5 papers
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…
Scalar curvature bounds for 3D continuous metrics through the Inverse Mean Curvature Flow
Mattia Fogagnolo, Giorgio Gatti, Alessandra Pluda
We propose a notion of scalar curvature lower bounds in a three-dimensional Riemannian manifold endowed with a metric based on the monotonicity of the Hawking mass along the…
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 be a complete, connected, non…
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 -cap…
A Note on Ricci-pinched three-manifolds
Luca Benatti, Carlo Mantegazza, Francesca Oronzio +1
Let be a complete, connected, non-compact Riemannian -manifold. Suppose that satisfies the Ricci--pinching condition f…