Calculus of Variations and Geometric Measure Theory

A. Carlotto - A. Mondino

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

created by mondino on 14 Jun 2016
modified on 14 Sep 2016


Journal of London Math. Society

Inserted: 14 jun 2016
Last Updated: 14 sep 2016

Year: 2016


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.