Bifurcation of minimal surfaces and the first eigenvalue of the Laplacian

• Grant number: 21/09650-4
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: November 01, 2021
• End date: October 29, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marcos Martins Alexandrino da Silva
• Grantee: Eduardo Rosinato Longa
• Supervisor: Joaquín Pérez Muñoz
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Universidad de Granada (UGR), Spain
• Associated to the scholarship: 21/03599-7 - From geometric analysis to bifurcation, BP.PD

Abstract

We intend to apply the techniques of bifurcation theory to prove local and global results concerning the existence of bifurcation minimal tori in Riemannian 3-manifolds which are products of a fixed closed surface and a circle of variable radius. Moreover, we will address the problems of giving examples and possibly characterizing extremal domains and surfaces for the first eigenvalue of the Laplacian. (AU)