Programação

Credenciamento: 13h - 13h50

Ernani Ribeiro Jr (UFC)

Solitons de Ricci gradientes shrinking em dimensão quatro

Resumo: Solitons de Ricci gradientes shrinking desempenham um papel fundamental no estudo da formação de singularidades no fluxo de Ricci e têm recebido considerável atenção nos últimos anos. Nesta palestra, abordaremos sólitons de Ricci gradientes shrinking em dimensão quatro. Apresentaremos uma condição ótima de pinching que força o soliton a ser localmente Kähler. Além disso, apresentaremos um teorema de caracterização e um teorema de gap integral ponderado para solitons de Ricci gradientes compactos. Esses resultados fazem parte de um trabalho conjunto com Xiaodong Cao e Hosea Wondo.

Matheus B. Martins (UNEAL)

Monotonicity in Warped Products and Applications

Resumo: In this work, we investigate the geometric and analytic properties of hypersurfaces

immersed in warped product spaces. Using a monotonicity formula, we establish new area estimates for properly embedded free-boundary hypersurfaces in dynamically expanding warped products. We also analyze the rigidity case, characterizing hypersurfaces that attain equality in our estimates. Additionally, we derive a monotonicity formula for c-solitons of the mean curvature flow, establish an area bound, and obtain a further linear isoperimetric inequality. Finally, we introduce a novel area estimate based on the density at infinity, providing new insights into the asymptotic behavior of minimal hypersurfaces.

Franciele Santos (UFS)

Eigenvalue estimates for Schrödinger operators on Ricci shrinkers.

Resumo: In this talk, we will study the problem of minimizing the lowest eigenvalue of two Schrödinger-type operators on a Ricci shrinker among all potentials satisfying certain conditions. For each of these operators, we will obtain an optimal lower bound for its lowest eigenvalue. We will prove that, for one of the operators, the bound is attained when the potential is a potential function of the Ricci shrinker, while for the other operator, the bound is attained when the potential is an affine function. This is a joint work with Xu Cheng, Neilha Pinheiro, and Detang Zhou.

Ivan Miranda (IMPA)

Ambient geometry via min-max widths of embedded circles

Abstract: We prove a lower bound for the Birkhoff min-max invariant of a Riemannian sphere in terms of the min-max width of its embedded circles. We establish related rigidity results characterizing the round spheres among Zoll spheres. Considering a non-compact complete Riemannian manifold, we relate upper bounds for the min-max width of its embedded circles to the existence of continuous functions to finite graphs with level sets that have uniformly bounded diameters. In the Euclidean plane, we bound from below the classical width of a simple closed curve by its min-max width. The proofs share a common strategy of inducing a sweepout in an embedded circle from a given ambient sweepout. This is a joint work with Lucas Ambrozio and Rafael Montezuma.

Jantar de confraternização [local a definir]: 18h - 21h

Pedro Gaspar (Pontifícia Universidad Católica de Chile)

TBA

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Maria Andrade (UFS)

Rigidity for V-static-type equations on manifolds with boundary

Abstract: In this talk, we study compact Riemannian manifolds with boundary subject to a V-static-type equation. By combining a generalized Reilly formula with Steklov-type boundary value problems, we establish new integral inequalities involving boundary geometric data. As a consequence, we obtain rigidity theorems, including characterizations of geodesic balls in space forms.

Rondinelle Batista (UFPI)

The positive mass theorem via level sets of harmonic functions

Abstract: In this talk, we present a proof of the positive mass theorem based on the study of level sets of harmonic functions for asymptotically flat 3-manifolds with non-compact boundary. If time permits, we will also discuss a geometric formula for the mass of asymptotically hyperbolic manifolds with non-compact boundary.

Benedito Leandro (UNB)

Fórmulas divergentes e Aplicações

Resumo: Irei falar sobre alguns trabalhos recentes que tratam da classificação de variedades do tipo Einstein, tais como solitons de Ricci, variedades estáticas e V-estáticas.

O método que usaremos para tratar esses problemas é o desenvolvimento de fórmulas divergentes que envolvem campos vetoriais sensíveis a estas variedades. Mostraremos também como tais fórmulas estão relacionadas com a teoria potencial de funções.

Márcio Santos (UFPB)

quasi-Einstein manifolds with constant scalar curvature.  

Abstract: In this talk, we study quasi-Einstein manifolds with constant scalar curvature. We provide a classification of compact and noncompact (possibly with boundary) T-flat quasi-Einstein manifolds with constant scalar curvature, where the T-tensor is directly related to the Cotton and Weyl tensors. In addition, we prove a complete classification of compact and noncompact (possibly with boundary) 3-dimensional m-quasi-Einstein manifolds with constant scalar curvature.

Álvaro Ramos (UFRGS)

Estabilidade dinâmica de horoesferas sob o fluxo da curvatura média

Resumo: Mostramos que as horoesferas são dinamicamente estáveis como soluções para o fluxo da curvatura média (FCM) no espaço hiperbólico $\mathbb{H}^{n+1}$ dadas por gráficos de Killing sobre uma hipersuperfície totalmente geodésica. Mais especificamente, mostramos que qualquer solução gráfica do FCM que inicialmente seja uma perturbação da horoesfera com decaimento $C^0$ no infinito se torna assintótica, com a evolução do fluxo, ao soliton de translação gerado por essa horoesfera. Trabalho em conjunto com Ronaldo de Lima.

Discussões sobre problemas em aberto