MATH Seminar
| Title: On Blow-ups of Compact Metrics and the Resulting Curvatures |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Pascal Philipp of Emory University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2011-11-15 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: On a compact Riemannian manifold with non-empty boundary, let a boundary defining function $\rho$ be given. Multiplying the compact metric by $\rho_{-2}$ defines a new metric. This conformal change, together with the interior of the original manifold, gives an infinite area Riemannian manifold $(M,g)$. The asymptotic behavior of the sectional curvatures of $g$ will be studied. The main result of these considerations will justify the use of asymptotically hyperbolic manifolds in fields of Mathematics and Physics. |
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