A free boundary minimal surface via a 6-sweepout
Abstract
We prove that the Almgren-Pitts 6-width of the unit 3-ball is less than 2π. We also prove that there exists a free boundary minimal surface in the unit 3-ball that has genus at most 1, index at most 5, area less than 2π, and is not the equatorial disk or the critical catenoid.
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