Quantitative estimates for the Dirichlet energy

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• Melanie Rupflin (University of Oxford)
• Tuesday 19 August 2025, 16:00-16:45
• Seminar Room 1, Newton Institute.

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DNMW06 - Recent challenges in the mathematical design of new materials

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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