Jonathan Zhu, Princeton
"Mean curvature flow and explicit Łojasiewicz inequalities"
In geometric PDE, Łojasiewicz inequalities have become a popular tool for studying the stability of solutions. The classical Łojasiewicz inequalities describe asymptotic behaviour of real analytic functions near their zero (or critical) set. The original proofs are quite involved, but in certain settings a Łojasiewicz inequality may be proven directly, with explicit asymptotics. We will discuss one such proof strategy based on Taylor expansion. The mean curvature flow is a geometric evolution equation describing the `heat flow’ of submanifolds. A major problem is to understand the singularities of the flow, which can be modelled on homothetically shrinking solitons. We will describe the realisation of the above strategy for certain shrinking cylinders and products of shrinking spheres, and consequences for the flow.
Zoom meeting: https://zoom.us/j/93201242542?pwd=YlJGRUxBTDB4S2tiYmN0ZEVabFRIdz09