-  Title : Common boundary values of holomorphic functions for two-sided complex structures.

: We will study the regularity of a continuous function F defined on the union of two smoothly bounded disjoint domains D_1, D_2 in C^n and their common boundary M. Assume that for i=1,2, the function F is holomorphic on D_i with respect to a smooth almost complex structure J_i which is defined on the union of D_i and M. Our main theorem shows that F is smooth on the union of D_1 with M, provided that the two almost complex structures are sufficiently close on M.

In the first lecture, we will give a short proof for the theorem when n=1. We will also prove a regularity result on J-holomorphic curves that depend on a parameter. In the second lecture, we will prove the full version of the theorem. This is joint work with Florian Bertrand and Jean-Pierre Rosay.

-  Date : 8 p.m. - 10 p.m. September 16th, 2013