These lecture notes have been written as an introduction to the
characteristic theory for two-dimensional Monge-Amp re equations, a
theory largely developed by H. Lewy and E. Heinz which has never
been presented in book form. An exposition of the Heinz-Lewy theory
requires auxiliary material which can be found in various
monographs, but which is presented here, in part because the focus
is different, and also because these notes have an introductory
character. Self-contained introductions to the regularity theory of
elliptic systems, the theory of pseudoanalytic functions and the
theory of conformal mappings are included. These notes grew out of
a seminar given at the University of Kentucky in the fall of 1988
and are intended for graduate students and researchers interested
in this area.
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