Topology of complete minimal submanifolds in ${\mathbb{R}}^{n+m}$ with finite total curvature

Abstract

In [CKM17], Chodosh, Ketover, and Maximo proved finite diffeomorphism theorems for complete embedded minimal hypersurfaces of dimension $⩽$ 6 with finite index and bounded volume growth ratio. In this paper, we adapt their method to study finite diffeomorphism types for complete immersed minimal submanifolds of arbitrary codimension in Euclidean space with finite total curvature and Euclidean volume growth.

24 pages