Events

Date: 24 September 2025   Time: 14:00 - 15:30

Location: MB503

Quantitative Stability Estimates for almost minimising maps of the Dirichlet Energy

A natural question in the study of many variational problems is the quantitative stability of minimisers, i.e. the question of whether, and at what rate, the distance to the set of minimisers can be controlled in terms of the energy defect. In this talk, I will present joint work with Professor Melanie Rupflin, which establishes quantitative stability estimates for degree one maps of the Dirichlet Energy from either the torus or hyperbolic surfaces into the sphere. While the classical question of quantitative stability fails due to the non-existence of degree one minimisers from the given surface, the existence of a "singular" minimiser consisting of a "bubble" and "base map" can be shown. In this work, we establish a quantitative stability estimate for this set of "singular" minimisers through a carefully constructed combined gradient flow that evolves both domain and map.