| EPSRC Reference: |
GR/S61522/01 |
| Title: |
Complete Einstein metrics of negative scalar curvature |
| Principal Investigator: |
Singer, Professor M |
| Other Investigators: |
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| Department: |
Sch of Mathematics |
| Organisation: |
University of Edinburgh |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
12 June 2003 |
Ends: |
11 June 2007 |
Value (£): |
8,418
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Analysis |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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For a compact manifold with boundary, Poincare-Einstein metrics are a natural object of study in differential geometry, extending the case of the standard hyperbolic metric on the closed unit ball. In the last few years, substantial progress towards a general theory was made in particular by Anderson, but many questions are left open. Indeed, the basic question of whether there are any obstructions to the existence of a PE metric on a given compact manifold with boundary remains open. In this project, we shall complement Anderson's results with new existence theorems for PE metrics on an interesting class of manifolds with boundary, obtained by filling spherical space-forms. In dimension 4, we shall also study boundary-value problems for self-dual Einstein metrics in order to obtain a general understanding of LeBrun's notion of 'positive-frequency conformal structure'. We also aim to study some of the various phenomena that occur when the boundary conformal structure is varied, and in particular when it is allowed to degenerate. The methods used will include (micro-local) analysis of PDEs, as well as ideas from geometry and topology.
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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.ed.ac.uk |