34 citations · 88 across the 23 of their papers we have counts for
10 papers · 1 filter
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…
Łojasiewicz-Simon inequalities for minimal networks: stability and convergence
Alessandra Pluda, Marco Pozzetta
We investigate stability properties of the motion by curvature of planar networks. We prove Lojasiewicz-Simon gradient inequalities for the length functional of planar networks wit…
Short-time existence for the network flow
Jorge Lira, Rafe Mazzeo, Alessandra Pluda +1
This paper contains a new proof of the short-time existence for the flow by curvature of a network of curves in the plane. Appearing initially in metallurgy and as a model for the…
Lectures on curvature flow of networks
Carlo MAntegazza, Matteo Novaga, Alessandra Pluda
We present a collection of results on the evolution by curvature of networks of planar curves. We discuss in particular the existence of a solution and the analysis of singularitie…
Evolution of networks with multiple junctions
Carlo Mantegazza, Matteo Novaga, Alessandra Pluda +1
We consider the motion by curvature of a network of curves in the plane and we discuss existence, uniqueness, singularity formation and asymptotic behavior of the flow.
Motion by curvature of networks with two triple junctions
Carlo Mantegazza, Matteo Novaga, Alessandra Pluda
We consider the evolution by curvature of a general embedded network with two triple junctions. We classify the possible singularities and we discuss the long time existence of the…