| EPSRC Reference: |
GR/M74665/01 |
| Title: |
EIGENVALUES OF ELLIPTIC OPERATORS ON RIEMANNIAN MANIFOLDS AND GRAPHS |
| Principal Investigator: |
Grigor'Yan, Professor A |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
23 June 1999 |
Ends: |
22 December 2001 |
Value (£): |
3,500
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The main aim of this project is to advance further the knowledge of the eigenvalues on manifolds and graphs. One of the primary objectives is obtaining Weyl-type bounds for higher eigenvalues of Laplace operators on compact Riemannian manifolds. Even for non-negatively curved manifolds the known results are incomplete. The second direction is obtaining Weyl-type lower bounds for higher Dirichlet eigenvalues of regions on manifolds under minimal hypotheses. This is related to the isoperimetric inequalities and Cheeger constants of balls. The third direction of research is obtaining lower bounds for the number of negative eigenvalues of Schrodinger operators in Euclidean space using the procedure of construction of capacitors. The same method is likely to give also new relations between the Dirichlet eigenvalues of a regions with the eigenvalues of its boundary. The fourth direction is creating a techniques for estimating eigenvalues on graphs based on estimates of the spring ratio for balls.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.imperial.ac.uk |