We prove optimal genus bounds for minimal surfaces arising from the min-max construction of Simon–Smith. This confirms a conjecture made by Pitts–Rubinstein in 1986.
The author was partially supported by NSF-PRF DMS-1401996 as well as by ERC-2011-StG-278940.
"Genus bounds for min-max minimal surfaces." J. Differential Geom. 112 (3) 555 - 590, July 2019. https://doi.org/10.4310/jdg/1563242473