The local picture theorem on the scale of topology

Abstract

We prove a descriptive theorem on the extrinsic geometry of an embedded minimal surface of injectivity radius zero in a homogeneously regular Riemannian three-manifold, in a certain small intrinsic neighborhood of a point of almost-minimal injectivity radius. This structure theorem includes a limit object which we call a minimal parking garage structure on ${\mathbb{R}}^3$, whose theory we also develop.

arXiv comment47 pages, 8 figures. Version accepted for publication in JDG