12 Sep 2002

Boris Kruglikov "Existence and non-existence results in almost complex geometry - I".

Almost complex geometry is a geometry defined by a non-integrable complex structure. Some statements from the complex geometry persist in the "almost" situation, but mainly those which are based on the holomorphic curves technique. I will give a review of the results and methods. In particular I will mention old joint results with M.Overholt on Kobayashi pseudodistance. The infinitesimal analog, Royden pseudonorm, requires an existence theorem for big pseudoholomorphic curves. I will present a short proof of this theorem.