| dc.identifier.uri | http://hdl.handle.net/11401/76417 | |
| 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 | This thesis is concerned with the question: given a submanifold (perhaps with singularities), when is it possible to change the metric in some specific way so that the submanifold becomes homologically mass-minimizing? \\ We studied this question for ``horizontal" change of metrics and conformal change of metrics for both compact and non-compact submanifolds. We also explored cases with singularities or boundaries. The main idea is to use the theory of calibrated geometry and gluing techniques. \\ As a special case, we confirm that any given oriented compact connected submanifold which is not $\mathbb{R}$-homologous to zero in a Riemannian manifold can be calibrated after a highly controlled conformal change of the given metric. The statement remains true for any non-connected submanifold as well provided the convex hull of $\mathbb{R}$-homology classes represented by its oriented connected components does not contain zero. | |
| dcterms.available | 2017-09-20T16:50:11Z | |
| dcterms.contributor | Lawson, Blaine | en_US |
| dcterms.contributor | Anderson, Michael | en_US |
| dcterms.contributor | LeBrun, Claude | en_US |
| dcterms.contributor | Grigorian, Sergey. | en_US |
| dcterms.creator | Zhang, Yongsheng | |
| dcterms.dateAccepted | 2017-09-20T16:50:11Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:11Z | |
| dcterms.description | Department of Mathematics. | en_US |
| dcterms.extent | 97 pg. | en_US |
| dcterms.format | Monograph | |
| dcterms.format | Application/PDF | en_US |
| dcterms.identifier | http://hdl.handle.net/11401/76417 | |
| dcterms.issued | 2015-08-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:11Z (GMT). No. of bitstreams: 1
Zhang_grad.sunysb_0771E_11322.pdf: 682115 bytes, checksum: 20ddbe0eab0a4890087b73e0dbe71b79 (MD5)
Previous issue date: 2013 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Calibrated geometry, conformal change, mass-minimizing | |
| dcterms.subject | Mathematics | |
| dcterms.title | Gluing Techniques in Calibrated Geometry | |
| dcterms.type | Dissertation | |
