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Title: Lipschitz control of geodesics in the Heisenberg group.

Abstract

Monge first posed his (L{sup 1}) optimal mass transfer problem: to find a mapping of one distribution into another, minimizing total distance of transporting mass, in 1781. It remained unsolved in R{sup n} until the late 1990's. This result has since been extended to Riemannian manifolds. In both cases, optimal mass transfer relies upon a key lemma providing a Lipschitz control on the directions of geodesics. We will discuss the Lipschitz control of geodesics in the (subRiemannian) Heisenberg group. This provides an important step towards a potential theoretic proof of Monge's problem in the Heisenberg group.

Authors:
Publication Date:
Research Org.:
Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1039023
Report Number(s):
SAND2010-8803C
TRN: US201209%%114
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Conference
Resource Relation:
Conference: Proposed for presentation at the Seventh International Conference on Differential Equations held December 15-18, 2010 in Tampa, FL.
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; DIFFERENTIAL EQUATIONS; DISTRIBUTION; GEODESICS; MASS TRANSFER

Citation Formats

Berry, Robert Dan. Lipschitz control of geodesics in the Heisenberg group.. United States: N. p., 2010. Web.
Berry, Robert Dan. Lipschitz control of geodesics in the Heisenberg group.. United States.
Berry, Robert Dan. 2010. "Lipschitz control of geodesics in the Heisenberg group.". United States.
@article{osti_1039023,
title = {Lipschitz control of geodesics in the Heisenberg group.},
author = {Berry, Robert Dan},
abstractNote = {Monge first posed his (L{sup 1}) optimal mass transfer problem: to find a mapping of one distribution into another, minimizing total distance of transporting mass, in 1781. It remained unsolved in R{sup n} until the late 1990's. This result has since been extended to Riemannian manifolds. In both cases, optimal mass transfer relies upon a key lemma providing a Lipschitz control on the directions of geodesics. We will discuss the Lipschitz control of geodesics in the (subRiemannian) Heisenberg group. This provides an important step towards a potential theoretic proof of Monge's problem in the Heisenberg group.},
doi = {},
url = {https://www.osti.gov/biblio/1039023}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Dec 01 00:00:00 EST 2010},
month = {Wed Dec 01 00:00:00 EST 2010}
}

Conference:
Other availability
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