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Dependence of best Riemannian constants in spaces of metrics

Grant number: 08/07368-5
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): January 01, 2009
Effective date (End): 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.

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