Mass Transportation on the Earth
50 pages
English

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Mass Transportation on the Earth

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50 pages
English
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Description

Mass Transportation on the Earth Ludovic Rifford Universite de Nice - Sophia Antipolis & Institut Universitaire de France UPV/EHU Ludovic Rifford Mass Transportation on the Earth

  • distance between

  • quadratic monge's

  • µ0

  • any measurable map

  • mass transportation

  • transport map

  • universite de nice


Sujets

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Publié par
Nombre de lectures 11
Langue English

Exrait

Mass
Transportation on the
Ludovic Rifford
Universit´edeNice-SophiaAntipolis & Institut Universitaire de France
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UPV/EHU
RiordaMssTransprotationont
Earth
heEarth
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LetMbe asmooth connected compact surfaceinRn. For anyx,yM, we define the geodesic distance betweenxand y, denoted byd(x,ythe minimum of the lengths of the), as curves (drawn onM) joiningxtoy.
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ransTmapsportsnarTssaMdroiRcEahentnoioatrtpodoviLutrh
Bmeasurable
Letµ0andµ1beprobability measuresonM. We call transport mapfromµ0toµ1any measurable map T:MMsuch thatT]µ0=µ1, that is µ1(B) =µ0T1(B),Bmeas
M.
atioportransassT
c(x,T(x))dµ0(x). M
Given two probabilities measuresµ0, µ1surM, find a transport mapT:MMfromµ0toµ1which minimizes the quadratic cost (c=d2/2) Z
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c(x,T(x))dµ0(x). M
Given two probabilities measuresµ0, µ1surM, find a transport mapT:MMfromµ0toµ1which minimizes the quadratic cost (c=d2/2) Z
Existence ?
Regularity ?
Uniqueness ?
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