Min-max free boundary minimal surface with genus at least one
Abstract
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.
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