Lipschitz control of geodesics in the Heisenberg group.
Conference
·
OSTI ID:1039023
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.
- Research Organization:
- Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1039023
- Report Number(s):
- SAND2010-8803C; TRN: US201209%%114
- 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
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