Optimisation problems in Spectral Geometry

• Grant number: 24/01663-8
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2024
• End date: April 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Eduardo Rosinato Longa
• Grantee: Eduardo Rosinato Longa
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated researchers: Pieralberto Sicbaldi

Abstract

This project aims to study certain eigenvalue optimisation problems in Riemannian manifolds. Firstly, we would like to prove the existence of extremal domains for the first eigenvalue of the Laplacian in complete, noncompact and geometrically bounded manifolds. Secondly, we intend to show that the presence of symmetries in a manifold prevents the existence of extremal metrics which are invariant by such symmetries. (AU)