Dependence of best Riemannian constants in spaces of metrics

• Grant number: 08/07368-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: January 01, 2009
• End date: August 31, 2009
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Paolo Piccione
• Grantee: Ezequiel Rodrigues Barbosa
• 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

The goal of this project is to study the continuity of the dependence of best constants in Sobolev embeddings in the space of all Riemannian metrics of a given differentiable manifold. The motivation for this research is given by the relations that the best constants in inequalities of Sobolev type have in geometrical problems like the Ricci flow, the Yamabe problem, and the isoperimetric inequalities.