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Melanie Rupflin (University of Oxford)
Tuesday 19 August 2025, 16:00-16:45
Quantitative estimates for the Dirichlet energy
- 👤 Speaker: Melanie Rupflin (University of Oxford)
- 📅 Date & Time: Tuesday 19 August 2025, 16:00 - 16:45
- 📍 Venue: Seminar Room 1, Newton Institute
Abstract
In this talk we discuss the question of quantitative stability of minimisers for the classical Dirichlet energy of maps from $R^2$ into the unit sphere, i.e. whether, and with what rate, the distance of a map which almost minimise the energy (with given degree) to the nearest minimiser can be bounded in terms of the energy defect. We will see that there is a marked difference between maps of degree 1 and maps of higher degree and will discuss how a more flexible approach to quantitative stability and specially designed gradient flows can be used to establish sharp quantitative stability results for maps for which energy concentrates at multiple scales and/or near multiple points.
Series This talk is part of the Isaac Newton Institute Seminar Series series.
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