Quantitative hyperbolicity of complex manifolds via numerical invariants (Duc Bao Nguyen - National University of Singapore)

We introduce numerical invariants measuring the hyperbolicity of Kahler manifolds, using directed positive currents. Basic properties of these invariants are studied and compared with the notion of hyperbolicity of Kobayashi, Brody and Demailly. We also show that if a complex manifold X satisfies Demailly's condition of negative jet curvature, then it is hyperbolic in our sense. We then compute some examples, discuss some related problems, as well as a list of open questions. This is a joint work with Tien-Cuong Dinh and Duc-Viet Vu.