Stability Properties of Rotational Catenoids in the Heisenberg Groups
Differential Geometry
2019-10-07 v3
Abstract
In this paper, we determine the maximally stable, rotationally invariant domains on the catenoids (minimal surfaces invariant by rotations) in the Heisenberg group with a left-invariant metric. We show that these catenoids have Morse index at least 3 and we bound the index from above in terms of the parameter . We also show that the index of tends to infinity with . Finally, we study the rotationally symmetric stable domains on the higher dimensional catenoids.
Cite
@article{arxiv.1010.0774,
title = {Stability Properties of Rotational Catenoids in the Heisenberg Groups},
author = {Pierre Bérard and Marcos P. Cavalcante},
journal= {arXiv preprint arXiv:1010.0774},
year = {2019}
}
Comments
Final version to appear in Matem\'atica Contempor\^anea (Sociedade Brasileira de Matem\'atica)