Quantitative estimates for the Dirichlet energy

by Melanie Rupflin (Oxford)

Monday Jun 2, 2025, 2:00 PM → 3:00 PM Europe/Paris

Salle Pellos (1R2-207)

In the analysis of variational problems it is often important to understand not only the behaviour of exact minimisers and critical points, but also of maps that almost minimise the energy or that almost solve the associated Euler-Lagrange equations.

 It is in particular natural to ask whether the distance of an almost minimiser to the nearest minimising state is controlled in terms of the energy defect and whether such a result not only holds in a qualitative, but in a sharp quantitative way.

In this talk we will discuss this and related questions for the classical Dirichlet energy of maps from surfaces into manifolds, in particular in the simple model problem of maps from the sphere $S^2$ to itself, for which minimisers (to given degree) are simply given by meromorphic functions in stereographic coordinates.