# Transportation of measures through branched networks at finite cost

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Eugene Stepanov
(St. Petersburg Branch of the Steklov Research Institute of Mathematics of the Russian Academy of Sciences)

created by gelli on 23 Nov 2007

28 nov 2007

**Abstract.**

Sala Riunioni--Dipartimento di Matematica--ore 17.00

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.