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 $\leqslant$ 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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Geometric and Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 February 2026
- Language
- EN
- Document type
- Preprint