34 citations · 88 across the 23 of their papers we have counts for
27 papers
One thousand and one higher-order geometric flows of networks
Luca Benatti, Alessandra Pluda
We show short-time existence and uniqueness up to reparametrization for a large class of higher-order geometric flows of curves and networks obtained as -gradient flow of high…
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…
Type-0 singularities in the network flow -- Evolution of trees
Carlo Mantegazza, Matteo Novaga, Alessandra Pluda
The motion by curvature of networks is the generalization to finite union of curves of the curve shortening flow. This evolution has several peculiar features, mainly due to the pr…