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Séminaire d'Analyse
Magnetic Brunn-Minkowski inequalities
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Europe/Paris
Amphi Schwartz
Amphi Schwartz
Description
In this talk, we will consider Minkowski averages on Riemannian manifolds where the interpolation is by action-minimizing magnetic geodesics with respect to a given magnetic potential. We will see that Brunn-Minkowski inequalities for this operation characterize lower bounds on a magnetic Ricci curvature. Examples include natural magnetic fields on K\"ahler and Sasakian manifolds, the former including as a special case a horocyclic Brunn-Minkowski inequality on complex hyperbolic space. We also observe that closed magnetic potentials from different cohomology classes may give rise to different geodesic Minkowski averages.