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Affine Dimension of Smooth Curves and Surfaces

Title: Affine Dimension of Smooth Curves and Surfaces.
Name(s): 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 department
Type of Resource: text
Genre: Text
Doctoral Thesis
Issuance: monographic
Date Issued: 2018
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (54 pages)
Language(s): English
Abstract/Description: 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.
Identifier: 2018_Sp_Williams_fsu_0071E_14512 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Spring Semester 2018.
Date of Defense: April 10, 2018.
Bibliography Note: Includes bibliographical references.
Advisory Committee: Richard Oberlin, Professor Directing Dissertation; Mike Ormsbee, University Representative; Alexander Reznikov, Committee Member; Martin Bauer, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record:
Host Institution: FSU

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Williams, E. R. (2018). Affine Dimension of Smooth Curves and Surfaces. Retrieved from