Sandra Huppert

Oberseminar Differentialgeometrie: Artemis Vogiatzi (University of London), Vortrag: High Codimension Mean Curvature Flow in $mathbb{C}P^n$.

Monday, 15.04.2024 16:00 im Raum SRZ 214

Mathematik und Informatik

Abstract: Mean curvature flow is a geometric evolution equation that describes how a submanifold embedded in a higher-dimensional space changes its shape over time. We establish a codimension estimate that enables us to prove at a singular time of the flow, there exists a rescaling that converges to a smooth codimension one limiting flow in Euclidean space, regardless of the original flow's codimension. Under a cylindrical type pinching, we show that this limiting flow is weakly convex and either moves by translation or is a self-shrinker. These estimates allow us to analyse the behaviour of the flow near singularities and establish the existence of the limiting flow. Considering the $\mathbb{C}P^n$, we go beyond the finite timeframe of the mean curvature flow, by proving that the rescaling converges smoothly to a totally geodesic limit in infinite time. Our approach relies on the preservation of the quadratic pinching condition along the flow and a gradient estimate that controls the mean curvature in regions of high curvature.

Angelegt am Thursday, 07.03.2024 10:39 von Sandra Huppert
Geändert am Monday, 11.03.2024 08:27 von Sandra Huppert
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