Asymptotically flat three-manifolds contain minimal planes

Abstract

Let $(M,g)$ be an asymptotically flat $3$-manifold containing no closed embedded minimal surfaces. We prove that for every point $p\in M$ there exists a complete properly embedded minimal plane in $M$ containing $p$.

final version, to appear in Adv. Math

References in corpus (2)

• On the finiteness of the Morse Index for Schrödinger operators
• On the number of minimal surfaces with a given boundary

Cited by in corpus (4)

• A dichotomy for minimal hypersurfaces in manifolds thick at infinity
• The Allen-Cahn equation on the complete Riemannian manifolds of finite volume
• Proper free-boundary minimal hypersurfaces with a rotational symmetry in the Schwarzschild space
• The space of partially free boundary minimal half disks