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Talks by Olaf Müller

New conformal methods in Riemannian and Lorentzian geometry

Universidad de Humboldt, Berlín

The talk gives an overview over some recently developed methods in global analysis and geometry that involve conformal factors. First we review a global existence result, obtained with Nicolas Ginoux, for Dirac-Higgs-Yang-Mills systems under the assumption that the underlying spacetime has a conformal extension, which ist the case for solutions to the Einstein equations for initial values in a weighted neighborhood of the standard ones. Then we switch to Riemannian geometry and show, using the novel ‚flatzoomer’ method, that every conformal class contains a metric of bounded geometry. Finally we sketch the consequences of the result for the Yamabe flow on noncompact manifolds and a related result for Cheeger-Gromov convergence of some relevance in the context of positive scalar curvature on compact manifolds.

Seminario 1ª planta, IEMath

Holonomía de variedades globalmente hiperbólicas

Universidad de Humboldt, Berlín

Aula A-23. 2ª Planta sección de Matemáticas

Olaf Müller

Universidad de Humboldt, Berlín

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