Gluing manifolds with boundary and bordisms of positive scalar curvature metrics

dc.contributor.advisor	Botvinnik, Boris
dc.contributor.author	Kazaras, Demetre
dc.date.accessioned	2017-09-06T21:47:27Z
dc.date.available	2017-09-06T21:47:27Z
dc.date.issued	2017-09-06
dc.description.abstract	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.	en_US
dc.identifier.uri	https://hdl.handle.net/1794/22698
dc.language.iso	en_US
dc.publisher	University of Oregon
dc.rights	All Rights Reserved.
dc.subject	Differential geometry	en_US
dc.subject	Scalar curvature	en_US
dc.title	Gluing manifolds with boundary and bordisms of positive scalar curvature metrics
dc.type	Electronic Thesis or Dissertation
thesis.degree.discipline	Department of Mathematics
thesis.degree.grantor	University of Oregon
thesis.degree.level	doctoral
thesis.degree.name	Ph.D.

Files

Now showing 1 - 1 of 1