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GAIA Seminar on Complex Analytic Geometry-Prof Xianghong Gong

posted Sep 11, 2013, 7:46 PM by Jihye Jung

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

-  Speaker : Prof. Xianghong Gong (U. Wisconsin-Madison, GAIA and POSTECH)
-  Abstract

: 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

-  Place : The GAIA (Math Science building room 106)
-  Contact: Jihye Jung (POSTECH, Tel. 279-8020)
Jihye Jung,
Sep 11, 2013, 7:48 PM