Our aim is to study the affine dimension of some smooth
manifolds. In Chapter 1, we review the notions of Minkowski and
Hausdorff dimension, and compare them with the lesser studied affine
dimension. In Chapter 2, we focus on understanding the affine dimension
of curves. In Section 2.1, we review the existing results for the
affine dimension of a strictly convex curve in the plane, and in
Section 2.2, we classify the smooth curves in ℝn based on affine
dimension. In Chapter 3, we classify the smooth hypersurfaces in ℝ3 with non-negative Gaussian curvature based on affine dimension, and in Chapter 4 we provide a lower and upper bound for the affine dimension of smooth, convex hypersurfaces in ℝn. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2018. / April 10, 2018. / Includes bibliographical references. / Richard Oberlin, Professor Directing Dissertation; Mike Ormsbee, University Representative; Alexander Reznikov, Committee Member; Martin Bauer, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_653530 |
| Contributors | Williams, Ethan Randy (author), Oberlin, Richard (professor directing dissertation), Ormsbee, Michael J. (university representative), Reznikov, Alexander (committee member), Bauer, Martin (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Mathematics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (54 pages), computer, application/pdf |
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