Events

Date: 8 October 2024   Time: 14:00 - 15:00

Location: MB503

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 in particular natural to ask whether an object with nearly minimal energy must essentially "look like" a minimiser, and if so whether this holds in a quantitative sense, i.e. whether one can bound the distance to the nearest minimiser in terms of the energy defect.
In this talk we will discuss this and related questions for the simple model problem of the Dirichlet energy of maps from the sphere $S^2$ to itself, where in stereographic coordinates the minimisers (to given degree) are given by meromorphic functions.