A non-existence result for minimal catenoids in asymptotically flat spaces

Abstract

We show that asymptotically Schwarzschildean 3-manifolds cannot contain minimal surfaces obtained by perturbative deformations of a Euclidean catenoid, no matter how small the ADM mass of the ambient space and how large the neck of the catenoid itself. Such an obstruction is sharply three-dimensional and ceases to hold for more general classes of asymptotically flat data.

Final version, to appear in Journal of the London Mathematical Society

References in corpus (2)

• Effective versions of the positive mass theorem
• The isoperimetric problem of a complete Riemannian manifolds with a finite number of $C^0$-asymptotically Schwarzschild ends

Cited by in corpus (2)

• Asymptotically flat three-manifolds contain minimal planes
• Proper free-boundary minimal hypersurfaces with a rotational symmetry in the Schwarzschild space