Equivariant min-max theory

Abstract

We develop an equivariant min-max theory as proposed by Pitts-Rubinstein in 1988 and then show that it can produce many of the known minimal surfaces in ${\mathbb{S}}^3$ up to genus and symmetry group. We also produce several new infinite families of minimal surfaces in ${\mathbb{S}}^3$ proposed by Pitts-Rubinstein. These examples are doublings and desingularizations of stationary integral varifolds in ${\mathbb{S}}^3$.

Cited by in corpus (2)

• Free boundary minimal surfaces of unbounded genus
• Min-max theory for constant mean curvature hypersurfaces