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Thesis

Estimates for small eigenvalues of the Laplacian and conformal Laplacian on closed manifolds

Abstract:

A central and well-established theme in geometry is eigenvalue estimates for geometric operators on manifolds. In this thesis we obtain new estimates for small eigenvalues of the Laplacian and conformal Laplacian respectively, in two distinct geometric contexts.


In the first part of this thesis we consider eigenvalues of the Laplacian on closed hyperbolic surfaces. It is known that for such surfaces degenerating by the collapse of a single simple closed geodesic, the first eige...

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Research group:
Oxford Centre for Nonlinear PDE
Oxford college:
Queen's College
Role:
Author

Contributors

Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Research group:
Oxford Centre for Nonlinear PDE
Oxford college:
Trinity College
Role:
Supervisor
ORCID:
0000-0002-9139-1400
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Research group:
Oxford Centre for Nonlinear PDE
Oxford college:
St Edmund Hall
Role:
Supervisor
ORCID:
0000-0002-1364-4433
More from this funder
Programme:
EPSRC Centre for Doctoral Training in Partial Differential Equations: Analysis and Applications
Funding agency for:
Chaudhary, A
Grant:
EP/L015811/1
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

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