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On two problems in analysis on manifolds

Author
Lu, Jinpeng
Published
[University Park, Pennsylvania] : Pennsylvania State University, 2019.
Physical Description
1 electronic document
Additional Creators
Burago, Dmitri, 1964-
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Open Access.
Summary
This dissertation contains meaningful results on two problems.1. I prove that the spectrum of the Laplace-Beltrami operator with the Neumann boundary condition on a compact Riemannian manifold with boundary admits a fast approximation by the spectra of suitable graph Laplacians on the manifold, and more generally similar graph approximation works for metric-measure spaces which are glued out of compact Riemannian manifolds of the same dimension.2. Given a diffeomorphism which is homotopic to the identity from the 2-torus to itself, we construct an isotopy whose norm is controlled by that of the diffeomorphism in question.
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Dissertation Note
Ph.D. Pennsylvania State University 2019.
Reproduction Note
Microfilm (positive). 1 reel ; 35 mm. (University Microfilms 13917938)
Technical Details
The full text of the dissertation is available as an Adobe Acrobat .pdf file ; Adobe Acrobat Reader required to view the file.
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