Stability of constant mean curvature surfaces in three dimensional warped product manifolds

Speaker: Gregório Silva Neto, UFAL.

Date: 13 nov 2019, 14h.

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: In this talk we will show that stable, compact without boundary, oriented, nonzero constant mean curvature surfaces in the de Sitter-Schwarzschild and Reissner-Nordstrom manifolds are the slices, provided its mean curvature satisfies some positive lower bound. More generally, we show that stable, compact without boundary, oriented nonzero constant mean curvature surfaces in a large class of three dimensional warped product manifolds are embedded topological spheres, provided the mean curvature satisfies a positive lower bound depending only on the ambient curvatures. We conclude showing that a stable, compact without boundary, nonzero constant mean curvature surface in a general Riemannian is a topological sphere provided its mean curvature has a lower bound depending only on the scalar curvature of the ambient space and the squared norm of the mean curvature vector field of the immersion of the ambient space in some Euclidean space.

 

A Hopf-Rinow Theorem for singular Riemannian spaces

Speaker: Matias del Hoyo, UFF.

Date: 11 oct 2019, 14h.

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: Differentiable stacks include manifolds and orbifolds as particular examples, and more general singular spaces. A theory of metrics over them has been recently proposed, with emphasis in their geodesic flows. In a joint work with M. de Melo (UFSCar) we explore the Riemannian geometry of these singular spaces, and develop singular version of classic results, including a Hopf-Rinow Theorem for stacks. I will overview the basics on differentiable stacks and their metrics, present our results explaining analogies and differences with the smooth case, and relate our contributions with previous works on geodesics of orbit spaces of actions and leaf spaces of foliations.

 

Monopólos de Haydys e Kapustin-Witten.

Speaker: Gonçalo Oliveira, UFF.

Date: 31 mai 2019, 14h30m.

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: As equações de monopólos mencionadas no título podem ambas ser interpretadas como certas complexificações da equação de monopólos usual. Nesta palestra vou introduzir e estudar esta equação de monopólos mais usual para depois explicar como,apesar da sua semelhança, as equações mencionadas no título têm teorias de existência muito distintas.

Trabalho em conjunto com Ákos Nagy.

 

Towards a Classification of Isoparametric Foliations

Speaker: Jianquan Ge, Beijing Normal University.

Date: 29 mar 2019, 14h30.

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: We will introduce classification results of isoparametric foliations on Riemannian manifolds, especially on unit spheres, 4-manifolds and exotic spheres, as well as some applications and related open problems.