214 citations · 485 across the 38 of their papers we have counts for
42 papers
Short-time existence for the Schouten flow
Giovanni Catino, Carlo Mantegazza
Let be a closed smooth Riemannian manifold, with . We prove short--time existence and uniqueness for the "critical" {\em Ricci--Bourguignon flow} \begin{e…
Uniform Sobolev, interpolation and geometric Calderón-Zygmund inequalities for graph hypersurfaces
Serena Della Corte, Antonia Diana, Carlo Mantegazza
In this note, our aim is to show that families of smooth hypersurfaces of which are all --close enough to a fixed compact, embedded one, have uniformly bound…
Stability for the Surface Diffusion Flow
Antonia Diana, Nicola Fusco, Carlo Mantegazza
We study the global existence and stability of surface diffusion flow (the normal velocity is given by the Laplacian of the mean curvature) of smooth boundaries of subsets of the $…
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…
Semilinear Li & Yau inequalities
Daniele Castorina, Giovanni Catino, Carlo Mantegazza
We derive an adaptation of Li & Yau estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We then apply these estimat…
A matrix Harnack inequality for semilinear heat equations
Giacomo Ascione, Daniele Castorina, Giovanni Catino +1
We derive a matrix version of Li \& Yau--type estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative sectional curvatures and parall…