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}
}
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