Minimal planes in asymptotically flat three-manifolds

Laurent Mazet (1) , Harold Rosenberg (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 IMPA - Instituto Nacional de Matemática Pura e Aplicada

In this paper, we improve a result by Chodosh and Ketover. We prove that, in an asymptotically flat $3$-manifold $M$ that contains no closed minimal surfaces, fixing $q\in M$ and a $2$-plane $V$ in $T_qM$ there is a properly embedded minimal plane $\Sigma$ in $M$ such that $q\in\Sigma$ and $T_q\Sigma=V$. We also prove that fixing three points in $M$ there is a properly embedded minimal plane passing through these three points.

Domaines: Géométrie différentielle [math.DG]

Laurent Mazet, Harold Rosenberg. Minimal planes in asymptotically flat three-manifolds. Journal of Differential Geometry, 2022, 120 (3), ⟨10.4310/jdg/1649953568⟩. ⟨hal-01768219⟩