Kobayashi conjecture on generic hyperbolicity

As a consequence one gets a surprising dichotomy for a residual (dense G δ ) subset of volume preserving C 1 diffeomorphisms on any compact manifold: the Oseledets splitting is

[42] Wolf (J.A.) – The action of a real semi-simple group on a complex flag manifold, I: Orbit structure and holomorphic arc

Since Proposition 1.2 is a special case of Theorem 1.6, and since the matrices A and B have been given in the special form of Assumption 3 in §5.1, the positivity of w A,B (x) for b

Later, Brock and Bromberg [BB] extended this result to prove that every finitely generated, freely indecomposable Kleinian group without parabolic elements is an algebraic limit

While the base dynamics of the Kontsevich–Zorich cocycle is the Teichm¨ uller flow on the space of translation surfaces, the basis of the Zorich cocycle is a renormalization dynamics

We then use this fact to confirm a long-standing conjecture of Kobayashi (1970), according to which a very general algebraic hypersurface of dimension n and degree at least 2n + 2

The first results in this direction are due to I.Graham [12], who gave boundary estimates of the Kobayashi metric near a strictly pseudoconvex boundary point, providing the

Hyperbolicity of generic high-degree hypersurfaces in complex projective space. Inventiones mathematicae, pages