Banca de DEFESA: NAÍSA CAMILA GARCIA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : NAÍSA CAMILA GARCIA
DATE: 23/09/2025
TIME: 10:00
LOCAL: https://meet.google.com/gnt-hrif-prb?authuser=1
TITLE:
PAGES: 93
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Geometria e Topologia
SPECIALTY: Geometria Diferencial
SUMMARY:

This work is divided into two independent parts, in the first we analyze the convergence of solutions of the Neumann problem for the Laplace-Beltrami operator posed in a thin domains in a sphere, which degenerate into an equator and feature a rapidly oscillating boundary. By applying the multiple scale method we derive the limit differential operator and using Tartar's approach obtain weak convergence of the solutions. Using an appropriate technique, we were able to construct asymptotic correctors, which not only ensure strong convergence but also provide explicit error estimates. Concluding the first part, we investigate the behavior of the eigenvalues and eigenfunctions through resolvent convergence. In the second part, we study the problem of optimizing the first eigenvalue of the Grushin Laplacian operator with Dirichlet and Neumann boundary conditions in isovolumetric domains on manifolds of the type R^m x N. In the case of Neumann boundary conditions, we consider the manifold R^m x N, endowed with the product metric g_can + g_N, where N is a compact manifold, and we show that among the isovolumetric domains, the cylinder of the form B_r x N  maximizes the first nonzero eigenvalue. In the case with Dirichlet boundary conditions, we prove the existence of domains that minimize the first eigenvalue both for manifolds of the type R^m x N and for manifolds of the type R^m x R^n endowed with the warped metric.

COMMITTEE MEMBERS:
Presidente - Interno ao Programa - 054.604.516-20 - MARCUS ANTONIO MENDONCA MARROCOS - UFAM
Membro Titular - Examinador(a) Externo à Instituição - ALESSANDRA APARECIDA VERRI - UFSCAR
Membro Titular - Examinador(a) Externo à Instituição - MARCONE CORREA PEREIRA - USP
Membro Titular - Examinador(a) Externo à Instituição - RAQUEL LEHRER - UNIOESTE
Membro Titular - Examinador(a) Externo à Instituição - SANDRA IMACULADA MOREIRA NETO - UEMA
Membro Suplente - Examinador(a) Interno ao Programa - 1882430 - STEFANO NARDULLI
Membro Suplente - Examinador(a) Externo à Instituição - JOSE NAZARENO VIEIRA GOMES - UFSCAR
Membro Suplente - Examinador(a) Externo à Instituição - ANTÔNIO AIRTON FREITAS FILHO - UFAM