Stability Properties of Rotational Catenoids in the Heisenberg Groups

Pierre Bérard (1) , Marcos P. Cavalcante (2)

1 IF - Institut Fourier
2 Instituto de Matematica - UFAL

In this paper, we determine the maximally stable, rotationally invariant domains on the catenoids $\cC_a$ (minimal surfaces invariant by rotations) in the Heisenberg group. We show that these catenoids have finite Morse index at least $3$ and we bound the index from above in terms of the parameter $a$. We also study the rotationally symmetric stable domains on the higher dimensional catenoids.

Mots clés: Minimal Surfaces; Heisenberg Group; Killing Fields; Index.; Index

Domaines: Géométrie différentielle [math.DG]

Pierre Bérard, Marcos P. Cavalcante. Stability Properties of Rotational Catenoids in the Heisenberg Groups. 2010. ⟨hal-00523308v1⟩