Prossimi seminari del Dipartimento di Matematica

The classical Gauss curvature flow was introduced by Firey in 1974 as an idealized model for the abrasion of convex stones under random collisions on a beach. In 1985, Kai-Seng Chou proved that convex hypersurfaces contract to a point in finite time under this flow. Later, in 1999, Ben Andrews showed that in two dimensions the rescaled flow converges to a round sphere. Subsequent works by Ben Andrews, Bennett Chow, Pengfei Guan, Lei Ni, and Brendle-Choi-Daskalopoulos established analogous convergence results in higher dimensions, as well as for the power Gauss curvature flow. In this talk, based on joint work with Xinqun Mei and Guofang Wang, we present convergence results for capillary variants of the Gauss curvature flow and power Gauss curvature flow under hydrophilic case.

A finite group G is nilpotent if and only if any two Sylow subgroups of coprime orders commute. In this talk we will discuss finite groups in which this property holds with high probability and we will see how this affects the structure of the group. In particular, we will see that the group $G$ is almost nilpotent in some precise sense.

We prove locali Holder continuity for non negative, locally bounded, local weak solutions for a class of doubly nonlinear parabolic equations. The novelty of the proof of such result Is given by the use of an expansion of positività argoment, combined with the study of an alternative (related tò DeGiorgi-type lemmas) and an exponential shift which allows us tò deal with the intrinsic geometry associated tò the problem. Seminario organizzato per il ciclo di seminari ASK

In this talk we discuss qualitative properties of weak solutions to a class of non-linear anisotropic parabolic partial differential equations. These equations arise in models where diffusion may behave differently in each spatial direction, leading to operators with direction-dependent growth and nonstandard structure. These results illustrate how classical tools from the De Giorgi–Nash–Moser theory can be adapted to anisotropic frameworks, providing a general approach to the study of nonlinear parabolic problems with direction-dependent diffusion.