Topological control for minmax free boundary minimal surfaces
Abstract
We establish general bounds on the topology of free boundary minimal surfaces obtained via minmax methods in compact, threedimensional ambient manifolds with mean convex boundary. We prove that the first Betti number is lower semicontinuous along minmax sequences converging in the sense of varifolds to free boundary minimal surfaces. In the orientable case, we obtain an even stronger result which implies that if the number of boundary components increases in the varifold limit, then the genus decreases at least as much. We also present several compelling applications, such as the variational construction of a free boundary minimal trinoid in the Euclidean unit ball.
 Publication:

arXiv eprints
 Pub Date:
 July 2023
 DOI:
 10.48550/arXiv.2307.00941
 arXiv:
 arXiv:2307.00941
 Bibcode:
 2023arXiv230700941F
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 35 pages, 5 figures