“Evolving geometries: an introduction to Mean Curvature Flow”
Wednesday 17 December 2025 h. 15:30 - Room 2BC30 - Gaia Bombardieri (Padova, Dip. Mat.)
Abstract
How do shapes evolve when driven by their mean curvature? In Euclidean space, Huisken’s classical theorem ensures that convex surfaces become spherical as they shrink to a point.
In this talk, we investigate the behavior of the flow in the sub-Riemannian setting of the Heisenberg group $H^1$. We will first introduce the basics of classical Mean Curvature Flow, focusing on the role of self-shrinkers as models for singularities. Then, we will move to the sub-Riemannian context, analyzing the flow for mean convex hypersurfaces. We will discuss the problem of self-similarity in this setting and present a recent result: the Pansu sphere, despite being the candidate isoperimetric profile of $H^1$, is not a self-shrinker. This reveals a striking divergence from the Euclidean intuition, where the static isoperimetric solution and the dynamic evolution profile coincide.
The video of the seminar will appear shortly afterwards in this Mediaspace channel.
