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UBC Theses and Dissertations
Inradius bounds for stable, minimal surfaces in 3-manifolds with positive scalar curvature Richardson, James
Abstract
Concrete topological properties of a manifold can be found by examining its geometry. Theorem 17 of his thesis, due to Myers [Mye41], is one such example of this; it gives an upper bound on the length of any minimizing geodesic in a manifold N in terms of a lower positive bound on the Ricci curvature of N, and concludes that N is compact. Our main result, Theorem 40, is of the same flavour as this, but we are instead concerned with stable, minimal surfaces in manifolds of positive scalar curvature. This result is a version of Proposition 1 in the paper of Schoen and Yau [SY83], written in the context of Riemannian geometry. It states: a stable, minimal 2-submanifold of a 3-manifold whose scalar curvature is bounded below by κ > 0 has a inradius bound of ≤√(8/3) π/√κ, and in particular is compact.
Item Metadata
Title |
Inradius bounds for stable, minimal surfaces in 3-manifolds with positive scalar curvature
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2012
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Description |
Concrete topological properties of a manifold can be found by examining its geometry. Theorem 17 of his thesis, due to Myers [Mye41], is one such example of this; it gives an upper bound on the length of any minimizing geodesic in a manifold N in terms of a lower positive bound on the Ricci curvature of N, and concludes that N is compact. Our main result, Theorem 40, is of the same flavour as this, but we are instead concerned with stable, minimal surfaces in manifolds of positive scalar curvature. This result is a version of Proposition 1 in the paper of Schoen and Yau [SY83], written in the context of Riemannian geometry. It states: a stable, minimal 2-submanifold of a 3-manifold whose scalar curvature is bounded below by κ > 0 has a inradius bound of ≤√(8/3) π/√κ, and in particular is compact.
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Genre | |
Type | |
Language |
eng
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Date Available |
2012-05-24
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution 3.0 Unported
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DOI |
10.14288/1.0072805
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2012-11
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution 3.0 Unported