Work

Topological control for min-max free boundary minimal surfaces

Year: 2026

Type: article

Abstract: We establish general bounds on the topology of free boundary minimal surfaces obtained via min-max methods in compact, three-dimensional ambient manifolds with mean convex boundary. We prove that the first Betti number is lower semicontinuous along min-max 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.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1800

Authors: Giada Franz, Mario B. Schulz

Institutions: Centre National de la Recherche Scientifique, Université Gustave Eiffel, University of Trento

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: European Commission

OpenAlex ID: W4383176637

FWCI:

Cites:

Cited by: 2

Related to: 10