Title:
Riemannian geometry of compact metric spaces
Riemannian geometry of compact metric spaces
| dc.contributor.advisor | Bellissard, Jean | |
| dc.contributor.author | Palmer, Ian Christian | en_US |
| dc.contributor.committeeMember | Bakhtin, Yuri | |
| dc.contributor.committeeMember | Belegradek, Igor | |
| dc.contributor.committeeMember | Cvitanovic, Predrag | |
| dc.contributor.committeeMember | Gangbo, Wilfrid | |
| dc.contributor.department | Mathematics | en_US |
| dc.date.accessioned | 2010-09-15T18:54:43Z | |
| dc.date.available | 2010-09-15T18:54:43Z | |
| dc.date.issued | 2010-05-21 | en_US |
| dc.description.abstract | A construction is given for which the Hausdorff measure and dimension of an arbitrary abstract compact metric space (X, d) can be encoded in a spectral triple. By introducing the concept of resolving sequence of open covers, conditions are given under which the topology, metric, and Hausdorff measure can be recovered from a spectral triple dependent on such a sequence. The construction holds for arbitrary compact metric spaces, generalizing previous results for fractals, as well as the original setting of manifolds, and also holds when Hausdorff and box dimensions differ---in particular, it does not depend on any self-similarity or regularity conditions on the space. The only restriction on the space is that it have positive s₀ dimensional Hausdorff measure, where s₀ is the Hausdorff dimension of the space, assumed to be finite. Also, X does not need to be embedded in another space, such as Rⁿ. | en_US |
| dc.description.degree | Ph.D. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1853/34744 | |
| dc.publisher | Georgia Institute of Technology | en_US |
| dc.subject | Noncommutative Geometry | en_US |
| dc.subject | Metric Spaces | en_US |
| dc.subject.lcsh | Geometry, Riemannian | |
| dc.subject.lcsh | Metric spaces | |
| dc.subject.lcsh | Hausdorff measures | |
| dc.title | Riemannian geometry of compact metric spaces | en_US |
| dc.type | Text | |
| dc.type.genre | Dissertation | |
| dspace.entity.type | Publication | |
| local.contributor.advisor | Bellissard, Jean | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
| relation.isAdvisorOfPublication | ba697900-ef37-4f7b-9e1e-c6fe69757c4d | |
| relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
| relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 |
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