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.
A non-existence result for minimal catenoids in asymptotically flat spaces / Carlotto, A.; Mondino, A.. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 95:2(2017), pp. 373-392. [10.1112/jlms.12012]
A non-existence result for minimal catenoids in asymptotically flat spaces
Carlotto A.;Mondino A.
2017-01-01
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.File in questo prodotto:
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