Thursday, September 22, 2022
5 p.m., on Zoom
Many interesting geometric objects are characterised as minimisers or critical points of natural geometric quantities such as the length of a curve, the area of a surface or the energy of a map. For the corresponding variational problems it is often important to not only analyse the existence and properties of potential minimisers, but to obtain a more general understanding of the energy landscape.
It is for example natural to ask whether an object that has energy very close to the minimal possible energy must also essentially "look like" a minimiser, and if so whether this holds in a quantitative sense, i.e. whether one can bound the distance to a minimiser in terms of the energy defect. Similarly one would like to understand whether for points where the gradient of the energy is very small one can hope to bound the distance of this point to the set of critical points in terms of the size of the gradient.
In this talk we will discuss some aspects of such quantitative estimates for geometric variational problems and their role in understanding the dynamics of the associated gradient flows.
