This thesis presents two main results on analytic and topological aspects of scalar curvature. The first is a gluing theorem for scalar-flat manifolds with vanishing mean curvature on the boundary. Our methods involve tools from conformal geometry and perturbation techniques for nonlinear elliptic PDE. The second part studies bordisms of positive scalar curvature metrics. We present a modification of the Schoen-Yau minimal hypersurface technique to manifolds with boundary which allows us to prove a hereditary property for bordisms of positive scalar curvature metrics. The main technical result is a convergence theorem for stable minimal hypersurfaces with free boundary in bordisms with long collars which may be of independent interest.
| Identifer | oai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/22698 |
| Date | 06 September 2017 |
| Creators | Kazaras, Demetre |
| Contributors | Botvinnik, Boris |
| Publisher | University of Oregon |
| Source Sets | University of Oregon |
| Language | en_US |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Rights | All Rights Reserved. |
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