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Pushing the boundaries of mathematics

A research project has advanced knowledge in mathematics through the study of the first eigenvalue problem for the Laplace operator in geometric settings. The work focused on the existence and properties of extremal metrics and has implications for a number of disciplines.
Pushing the boundaries of mathematics
An EU-funded research project, 'Geometry and analysis of the first eigenvalue functional' (GAFEF), funded an individual research fellowship to investigate this fast-developing area. Although it borders numerous research areas, only isolated results have previously been proved to a rigorous level.

With relevance to both pure and applied mathematics, GAFEF addressed questions related to the existence of maximal metrics, regularity theory and concentration–compactness properties.

The researcher developed an approach based on the calculus of variations. Results included the first eigenvalue and regularity theory on the so-called weakly conformal metrics and a new concentration–compactness phenomenon for sequences of extremal metrics.

Project results and research methods are relevant to experts from various disciplines. These include spectral geometry and especially geometric problems in spectral theory and calculus of variations.

This research and its outcomes should stimulate new work and further innovation from the EU's mathematical and scientific communities.

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