2022/03/12 by Sun, Yuchin
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2203.06305
In this paper, we build up a min-max theory for minimal surfaces using sweepouts of surfaces of genus g≥ 1 and m≥ 1 ideal boundary components. We show that the width for the area functional can be achieved by a bubble tree limit consisting of branched genus g free boundary minimal surfaces with nodes, and possibly finitely many branched minimal spheres and free boundary minimal disks.