G. Khimshiashvili

Hyper-Holomorphic Cells and Fredholm Theory

abstract:
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.