Séminaires : Séminaire de Géométrie

Equipe(s) : gd,
Responsables :L. Hauswirth, P. Laurain, R. Souam, E. Toubiana
Email des responsables :
Salle : https://bbb-front.math.univ-paris-diderot.fr/recherche/pau-6ha-of4-mea
Adresse :Sophie Germain

Archive avant 2014

Hébergé par le projet Géométrie et Dynamique de l’IMJ-PRG



Orateur(s) Miguel MANZANO - Universidad de Jaèn, Espagne,
Titre A construction of constant mean curvature surfaces in H2 X R
Horaire13:30 à 15:00
RésumeFor each 0 < H ≤ 1 and for each integer k ≥ 2, we show the existence of a 2- parameter family of properly Alexandrov-embedded surfaces with constant mean curvature H in H2 × R which are symmetric with respect to a horizontal slice and k vertical planes disposed symmetrically. These surfaces are obtained from solutions to Jenkins-Serrin problems in \tilde{SL2}(R) or Nil3 via the Daniel sister correspondence. We recover Plehnert’s (H,k)-noids and generalize Rodrıguez and Morabito’s minimal saddle towers. We also obtain new complete examples that we call (H, k)-nodoids, whose k ends are asymptotic to vertical cylinders from the convex side. These (H, k)-nodoids show that the so-called Krust property for minimal graphs obtained by Hauswirth, Sa Earp and Toubiana, does not extend to the case of positive constant mean curvature, i.e., there are minimal graphs over convex domains of \tilde{SL2}(R) and Nil3 whose conjugate surfaces are not embedded. 􏰋 􏰋
AdresseSophie Germain