Anton Savin

Differential equations on complex manifolds (joint talk by A.Yu. Savin and B.Yu. Sternin)

In this talk we deal with the theory of differential equations on complex manifolds. Namely, we study linear differential equations in C^N and, more generally, on complex manifolds. This theory is remarkable and interesting. It turns out that to study equations on complex manifolds, one has to use essentially new methods, than in the classical (real) theory. These methods will be described in the talk, in particular, we shall describe Sternin-Shatalov transform, which enables one to solve equations with constant coefficients.

Complex theory has important applications in mathematics and physics. In particular, we shall show how the methods described in the talk enable one to solve balayage inwards problem (Poincaré).