• Citer

Dirichlet problem for f-minimal graphs

par Casteras, Jean-Baptiste ;Heinonen, Esko;Holopainen, Ilkka
Référence Journal d'analyse mathématique, 138, 2, page (917-950)
Publication Publié, 2019-10

Article révisé par les pairs

• Détails
• Contenu

Résumé :

We study the asymptotic Dirichlet problem for f-minimal graphs in Cartan-Hadamard manifolds M.f-minimal hypersurfaces are natural generalizations of self-shrinkers which play a crucial role in the study of mean curvature flow. In the first part of this paper, we prove the existence of f-minimal graphs with prescribed boundary behavior on a bounded domain Ω ⊂ M under suitable assumptions on f and the boundary of Ω. In the second part, we consider the asymptotic Dirichlet problem. Provided that f decays fast enough, we construct solutions to the problem. Our assumption on the decay of f is linked with the sectional curvatures ofM. In view of a result of Pigola, Rigoli and Setti, our results are almost sharp.