Minimal surfaces with rapid area growth

Abstract

We give examples of proper minimal immersions in Euclidean space with very rapid area growth. The first is a proper embedding into ${\mathbf{R}}^4$ that yields a stable minimal surface, while the second is a proper immersion into ${\mathbf{R}}^3$. These results are motivated by [CM1] that shows that proper minimal submanifolds confined in space satisfy strong structural constraints.

Example added. Background added