Renato Feres (Washington University)

Foliated Liouville theorems.

Abstract. It is an elementary and well-known fact that a holomorphic function on a compact complex manifold without boundary is constant. In the setting of compact foliated spaces with (not necessarily compact) complex leaves, it becomes necessary to take into account the foliation dynamics in order to understand whether and to what extend continuous leafwise holomorphic functions are leafwise constant. The talk will describe a number of results in this direction due to A. Zeghib and the speaker.