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Min-max minimal surfaces in 3-manifolds

Author(s)
Ketover, Daniel
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Massachusetts Institute of Technology. Department of Mathematics.
Advisor
Tobias H. Colding.
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M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582
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Abstract
A Heegaard splitting of a 3-manifold gives rise to a natural set of sweepouts which by the Almgren-Pitts and Simon-Smith min-max theory generates a min-max sequence converging as varifolds to a smooth minimal surface (possibly disconnected, and with multiplicities). We prove a conjecture of Pitts-Rubinstein about how such a min-max sequence can degenerate; namely we show that after doing finitely many disk surgeries and isotopies on the sequence, and discarding some components, the remaining components are each isotopic to one component (or a double cover of one component) of the min-max limit. This convergence immediately gives rise to new genus bounds for min-max limits. Our results can be thought of as a min-max analog to the theorem of Meeks-Simon-Yau on convergence of a minimizing sequence of surfaces in an isotopy class.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
 
35
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (pages 51-54).
 
Date issued
2014
URI
http://hdl.handle.net/1721.1/90188
Department
Massachusetts Institute of Technology. Department of Mathematics.
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

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  • Mathematics - Ph.D. / Sc.D.

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