Generic properties and spectral theory for the Laplacian in Lorentzian and Finslerian geometry

• Grant number: 10/00067-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Duration: March 29, 2010 - August 22, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paolo Piccione
• Grantee: Paolo Piccione
• Visiting researcher: Leonardo Biliotti
• Visiting researcher institution: Università degli Studi di Parma, Italy
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 07/03192-7 - Submanifold geometry and Morse theory in finite and infinite dimensions, AP.TEM

Abstract

In this project, we have two goals. First, we want to develop a spectral theory for the Laplace operator of manifolds endowed with a non positive definite metric. We will try to find conditions that guarantee that such operator is discrete. As an application, we plan to prove the genericity of some properties of the isometry group of a compact Lorentz manifold. In the second part of the project we want to prove a Finsler version of the bumpy metric theorem. (AU)