On the asymptotic behavior of minimal surfaces in H²×R

Benoit R. Kloeckner (1) , Rafe Mazzeo (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Department of Mathematics

We consider the asymptotic behavior of properly embedded minimal surfaces in the product of the hyperbolic plane with the line, taking into account the fact that there is more than one natural compactification of this space. This provides a better setting in which to consider the general problem of determining which curves at infinity are the asymptotic boundary of such minimal surfaces. We also construct some new examples of such surfaces and describe the boundary regularity.

Mots clés: minimal surfaces; symmetric spaces; boundary

Domaines: Géométrie différentielle [math.DG]

Benoit R. Kloeckner, Rafe Mazzeo. On the asymptotic behavior of minimal surfaces in H²×R. 2015. ⟨hal-01161629⟩