Geometry and Topology Seminar

Anton Iliashenko, Beijing Institute of Mathematical Sciences and Applications

Hyperbolicity and Schwarz Lemmas in Calibrated Geometry

We will define two new notions of hyperbolicity for a general Riemannian manifold equipped with a calibration, which generalize the notions of Kobayashi and Brody hyperbolicity from complex geometry. For this we introduce a decreasing Finsler pseudo-metric that specializes to the Kobayashi-Royden pseudo-metric in the Kahler case; and derive the generalization of the classical Schwarz Lemma but for Smith immersions. We will talk about how these notions of hyperbolicity relate to one another and will see some examples. This is joint work with Kyle Broder and Jesse Madnick.

MC 5417