Eugene Stepanov (Univ. San Pietroburgo)  
``Transportation of measures through branched networks at finite cost''

ABSTRACT: The following transportation problem is studied: characterize
those couples of finite Borel measures with compact supports in a Euclidean
space that can be transported to each other at a finite fractional cost,
given by a fractional mass of  real one-dimensional normal currents. Besides
the class of
irrigable measures (i.e. measures which can be transported to a Dirac
measure
with the appropriate total mass at a finite cost), two other important
classes
of measures related to the problem are studied  which in a certain sense are
complementary to each other.