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DYNAMIC ISOPERIMETRY ON GRAPHS AND WEIGHTED RIEMANNIAN MANIFOLDS

Part of: Classical differential geometry Global differential geometry Partial differential equations on manifolds; differential operators Smooth dynamical systems: general theory

Published online by Cambridge University Press:  15 August 2018

ERIC KWOK
ERIC KWOK*
Affiliation:
School of Mathematics and Statistics, University of New South Wales Sydney, NSW 2052, Australia email e.kwok@unsw.edu.au
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Abstract

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Keywords

dynamical systemsisoperimetryLagrangian coherent structuresCheeger inequality

MSC classification

Primary: 37C60: Nonautonomous smooth dynamical systems
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions 53A10: Minimal surfaces, surfaces with prescribed mean curvature 58J50: Spectral problems; spectral geometry; scattering theory

Information

Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 514 - 515
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

Thesis submitted to the University of New South Wales in September 2017; degree approved on 20 February 2018; supervisor Gary Froyland.

References

Froyland, G., ‘Dynamic isoperimetry and the geometry of Lagrangian coherent structures’, Nonlinearity 28(10) (2015), 3587–3622.Google Scholar
Froyland, G. and Kwok, E., ‘Partitions of networks that are robust to vertex permutation dynamics’, Spec. Matrices 3(1) (2015), 22–42.Google Scholar
Froyland, G. and Kwok, E., ‘A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds’, J. Nonlinear Sci. (to appear), 83 pages, available online at https://link.springer.com/article/10.1007/s00332-017-9397-y.Google Scholar