Banca de DEFESA: CARLOS ALBERTO SANTOS BARBOSA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : CARLOS ALBERTO SANTOS BARBOSA
DATE: 16/04/2021
TIME: 10:00
LOCAL: https://meet.google.com/nky-qpjf-kbs
TITLE:

PARABOLICITY, SPACES OF HARMONIC FUNCTIONS AND TOPOLOGY AT INFINITY OF A COMPLETE MANIFOLD

KEY WORDS:

Harmonic functions, Topology at infinity, Parabolicity, Rigidity results.

PAGES: 78
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Geometria e Topologia
SPECIALTY: Geometria Diferencial
SUMMARY:

The aim of this work is to investigate the intrinsic relationship between certain spaces of harmonic functions on a complete manifold and their topology in the infinite. Assuming appropriate bounds on the Ricci curvature, we obtain estimates for the solutions of the Laplace and heat equations. This theory has important applications to geometry and topology of manifolds, some of which are presented here. In a manifold with more than one end, we have built a space of harmonic functions with remarkable properties. In turn, estimating the dimension of this space through geometric considerations will help us to understand the topology in the infinite of the manifold. More specifically, we will show a generalization of the celebrated Cheeger-Gromoll Splitting theorem.

BANKING MEMBERS:
Presidente - 2346971 - MARCOS RANIERI DA SILVA
Interno - 1165266 - FELICIANO MARCILIO AGUIAR VITORIO
Externo à Instituição - MARCIO SILVA SANTOS - UFPB