| dc.identifier.uri | http://hdl.handle.net/11401/76408 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | We study sequences of oriented Riemannian manifolds with boundary and, more generally, integral current spaces and metric spaces with boundary. We prove theorems demonstrating when the Gromov-Hausdorff [GH] and Sormani-Wenger Intrinsic Flat [SWIF] limits of sequences of such metric spaces agree. Thus in particular the limit spaces are countably $\mathcal{H}^n$ rectifiable spaces. From these theorems we derive compactness theorems for sequences of Riemannian manifolds with boundary where both the GH and SWIF limits agree. For sequences of Riemannian manifolds with boundary we only require nonnegative Ricci curvature, upper bounds on volume, noncollapsing conditions on the interior of the manifold and diameter controls on the level sets near the boundary. In addition we survey prior results of the author concerning the SWIF limits of manifolds with boundary, prior work of the author with Sormani concerning glued limits of metric spaces with boundary, prior work of the author with Li concerning GH and SWIF limits agreeing for Alexandrov spaces without boundary and work of Kodani, Anderson-Katsuda-Kurylev-Lassas-Taylor, Wong, and Knox concerning limits of Riemannian manifolds with boundary. | |
| dcterms.available | 2017-09-20T16:50:11Z | |
| dcterms.contributor | Lawson, Blaine | en_US |
| dcterms.contributor | Anderson, Michael | en_US |
| dcterms.contributor | Fukaya, Kenji | en_US |
| dcterms.contributor | Sormani, Christina. | en_US |
| dcterms.creator | Perales Aguilar, Raquel del Carmen Perales | |
| dcterms.dateAccepted | 2017-09-20T16:50:11Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:11Z | |
| dcterms.description | Department of Mathematics. | en_US |
| dcterms.extent | 71 pg. | en_US |
| dcterms.format | Monograph | |
| dcterms.format | Application/PDF | en_US |
| dcterms.identifier | http://hdl.handle.net/11401/76408 | |
| dcterms.issued | 2015-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:11Z (GMT). No. of bitstreams: 1
PeralesAguilar_grad.sunysb_0771E_12261.pdf: 690464 bytes, checksum: 42e4011bad2d30566530dc8a9e46f1f1 (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Mathematics | |
| dcterms.subject | Gromov-Hausdorff distance, Intrinsic Flat distance, Manifolds with Boundary, Metric Geometry, Rectifiable limits, Riemannian Geometry | |
| dcterms.title | Convergence of Manifolds and Metric Spaces with Boundary | |
| dcterms.type | Dissertation | |
