G. Khimshiashvili

Hyper-Holomorphic Cells and Fredholm Theory

We deal with differentiable cells defined by solutions to certain linear elliptic systems of first order. It turns out that in some cases families of such cells attached to a given submanifold may be described by Fredholm operators in appropriate function spaces. Using the previous results of the author on the existence of elliptic Riemann--Hilbert problems for generalized Cauchy--Riemann systems, we indicate some classes of systems which give rise to non-linear Fredholm operators of such type.