Berry, Robert Dan
(2009)
Lipschitz Estimates for Geodesics in the Heisenberg Group.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
In many modern approaches to solving Monge's mass transport problem (that is, optimal transport with respect to linear costs) in various metric spaces, one attempts to reduce the problem to one dimension by decomposing the measures along so-called transport (geodesic) rays. Certain key Lipschitz estimates on geodesics are needed in order provide such a decomposition. Herein these estimates for the (three dimensional, sub-Riemannian) Heisenberg Group are provided as a step towards solving Monge's problem in this metric space.
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Details
| Item Type: |
University of Pittsburgh ETD
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| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
30 June 2009 |
| Date Type: |
Completion |
| Defense Date: |
9 April 2009 |
| Approval Date: |
30 June 2009 |
| Submission Date: |
22 April 2009 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Carnot group; Heisenberg group; horizontal curve; Monge-Kantorovich; optimal mass transportation; subRiemannian geodesics |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-04222009-072017/, etd-04222009-072017 |
| Date Deposited: |
10 Nov 2011 19:40 |
| Last Modified: |
15 Nov 2016 13:41 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/7500 |
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