title: On focal stability in dimension two.
abstract: In Kupka et al. 2006 appears the Focal Stability Conjecture: the focal decomposition of the generic Riemann structure on a manifold M is stable under perturbations of the Riemann structure. In this paper, we prove the conjecture when M has dimension two, and there are no conjugate points.
authors.affiliation: Instituto de Matemática Pura e Aplicada, Rio de Janeiro, RJ, 22460-320, Brasil. peixoto@impa.br
authors.forename: Mauricio M
authors.initials: MM
authors.lastname: Peixoto
authors.forename: Charles C
authors.initials: CC
authors.lastname: Pugh