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Skip to Search Results- 2Riemannian Geometry
- 1Asymptotically Hyperbolic
- 1Bakry-Émery Ricci
- 1Differential Geometry
- 1Horowitz and Myers Conjecture
- 1Hyperbolic Space
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Fall 2021
A classic result in the field of Riemannian Geometry is the Splitting Theorem of Cheeger and Gromoll. Since this result there have been numerous alternate versions under a variety of different conditions. Continuing in this vein, we prove structure results on manifolds with boundary components...
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Numerical simulation of Ricci flow on a class of manifolds with non-essential minimal surfaces
DownloadFall 2011
In the last three decades, the Ricci flow has proved to be an extremely useful tool in mathematics and physics. We explore numerically the long time existence of the Ricci-DeTurck flow and the List flow for a one-parameter family of Riemannian manifolds with non-essential minimal surfaces. This...
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Fall 2012
In this thesis, we generalize the notion of asymptotically hyperbolic mass (first introduced by Wang in 2001) to manifolds with toroidal ends. Using this generalized definition, we show that under a normalized Ricci flow with asymptotically hyperbolic, conformally compact initial data with a...