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• W1607227891 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. Thesis Supervisor: Tobias H. Colding Title: Cecil and Ida Green Distinguished Professor of Mathematics" @default.
• W1607227891 created "2016-06-24" @default.
• W1607227891 creator A5024143049 @default.
• W1607227891 date "2014-01-01" @default.
• W1607227891 modified "2023-09-23" @default.
• W1607227891 title "Min-max minimal surfaces in 3-manifolds" @default.
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• W1607227891 hasPublicationYear "2014" @default.
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