The SAGE research workshops are preceded by events designed
to help graduate students benefit from workshop participation. During the
spring 2010 semester, Davi Maxio
helped prepare for SAGE 2010 by giving the following talk at the Junior Geometry Seminar.
Title: The
Monge problem with quadratic cost on compact
manifolds
Speaker: Davi Maximo (UT-Austin)
Abstract: Roughly
speaking, the Monge transportation problem seeks to
minimize the cost of transporting mass in a space, where the cost to transport
one unit of mass from location x to location y≠x
is given by a function C(x,y)>0.
In this talk, we present an existence and uniqueness result of Robert McCann
for the case that the space is a compact Riemannian manifold, and the cost
function is distance squared.
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