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Lipschitz Estimates for Geodesics in the Heisenberg Group

Berry, Robert Dan (2009) Lipschitz Estimates for Geodesics in the Heisenberg Group. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Berry, Robert
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairManfredi, Juanmanfredi@pitt.eduMANFREDI
Committee MemberVainchtein, Annaaav4@pitt.eduAAV4
Committee MemberBoyanovsky, Danielboyan@pitt.eduBOYAN
Committee MemberBeatrous, Frankbeatrous@pitt.eduBEATROUS
Committee MemberHajlasz, Piotrhajlasz@pitt.eduHAJLASZ
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:, etd-04222009-072017
Date Deposited: 10 Nov 2011 19:40
Last Modified: 15 Nov 2016 13:41


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