A basic construction in complex analysis is the Cauchy integral,
which provides a representation for holomorphic functions using their
values along a curve.  In higher dimensions, there are various
generalizations of the Cauchy integral.  These typically take
advantage of the geometry of the underlying domain.  Focusing on
dimension two, we'll consider one of the constructions, the Leray
integral, along with its basic analytic properties.  Using Mobius
invariance, we'll suggest that it's the most natural extension of the
Cauchy integral to higher dimensions.  This then leads to the problem
of understanding the Mobius geometry of a real hypersurface in C^n.