Quantidades conservadas em Relatividade Geral: o caso de dados iniciais com fronteira não-compacta

Speaker: Levi de Lima, UFC.

Date: 11 feb 2020, 14h.

Place: Room 205, Bloco H, Campus Gragoatá, UFF.

Abstract: Sabe-se que considerações de simetria, baseadas na existência de certas cargas de Noether, levam à definição de várias quantidades conservadas (energia, momento linear, centro de massa, etc.) para soluções das equações de campo de Einstein associadas a dados iniciais assintoticamente planos, e uma parte considerável do progresso em Relatividade Matemática nas últimas décadas consistiu em estabelecer propriedades fundamentais para tais quantidades (teoremas de massa positiva, desigualdades de Penrose, etc.). Nesta palestra, inicialmente recordamos esta teoria clássica e então indicamos como alguns de seus aspectos podem ser estendidos ao contexto em que o dado inicial possui fronteira não-compacta (trabalho conjunto com S. Almaraz, E. Barbosa e L. Mari). Nossa apresentação enfatiza as aplicações à Análise Geométrica (problema de Yamabe) e pretende ser acessível a uma audiência variada.

 

Geometry Day IV

Date: 29 nov 2019, 11h30.

Place: 4th Floor, Bloco H, Campus Gragoatá, UFF.

"Geometry Day" is a (semi)annual event directed to explore cutting edge research in contemporary Geometry. Researchers of diverse backgrounds participate in the event, providing a panoramic view of many topics, and further promoting our institute's international profile.

Program:

11.30-12.30 - Ilkka Holopainen (Helsinki): "Asymptotic Plateau problem for prescribed mean curvature hypersurfaces"
12.30-14.00 - Almoço
14.00-15.00 - Pedro Manfrim (Unicamp): "Weak Higgs-Hermite-Einstein metrics over ACyl manifolds"
15.00-15.30 - Pausa
15.30-16.30 - Matias del Hoyo (Uff): "An overview on Poisson and Dirac geometries"

Previous Editions:

• GD 0: Reimundo Heluani (IMPA), Letterio Gatto (Torino, IT), Lázaro Rodríguez (UFRJ)
• GD I: Alessia Mandini (PUC-Rio), Gonçalo Oliveira (UFF), Ethan Cotterill (UFF)
• GD II: Cecília Salgado (UFRJ), Dmitri Panov (King’s College London, UK), Vinícius Ramos (IMPA)
• GD III: Maria Amélia Salazar (UFF), Misha Verbitsky (IMPA/HSE), Liviu Ornea (Bucharest, RO).

 

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.

 

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.

 

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