## Min-max minimal surfaces in 3-manifolds

##### Author(s)

Ketover, Daniel
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##### Other Contributors

Massachusetts Institute of Technology. Department of Mathematics.

##### Advisor

Tobias H. Colding.

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Show full item record##### 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##### Department

Massachusetts Institute of Technology. Department of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.