Compactness for minimal surfaces with injectivity radius bounded from below

Abstract

We prove a compactness theorem for the space of closed embedded minimal surfaces with area bounded from above and injectivity radius bounded from below in a closed Riemannian $3$-manifold. This result is a variant of the Choi--Schoen compactness theorem in which the genus bound is replaced by a lower bound on the injectivity radius of the surface.