Riemannian geometry
Here are the main themes our group is currently working on.
Analysis on manifolds
- Eigenvalues of operators (Laplace, Schrodinger); geometric approach to the spectrum of differential operators on manifolds);
- Overdetermined elliptic problems;
- Yamabe equation, mass;
Equations of physics
- General relativity equations;
- Lorentz manifolds
Minimal or constant mean curvature submanifolds
- Constant mean curvature (hyper)surfaces;
- Minimal surfaces in $\mathbb{R}^4$ and their singularities;
- Families of codimension 2 minimal submanifolds
Interaction with other fields
- Physics: general relativity, quantum mechanics, wave equation
- Analysis: optimal transport, PDE's.
- Topology: knots and braids
Projects
- ANR-07-BLAN-0251-01 - Flots et Opérateurs Géométriques (Flows and geometric operators)
- Projet PHC France-Suisse Germaine de Stael : Approche géométrique du spectre d'opérateurs différentiels naturels sur les variétés (Franco-Swiss Project Germaine de Stael)
- Projet PHC France-Chine « Découverte Chine » (France-China PHC project: Discovering China)
- ANR-10-BLAN 0105 "Aspects Conformes de la géométrie" (Conformal aspects of geometry)
- ANR-12-BS01-012-01 - "Analyse Asymptotique en Relativité Générale" (Asymptotic analysis in General Relativity)
- ANR-11-IS01-0002 - Surfaces
- International Doctoral Seminar “Pythagoras of Samos”
- PHC CAPES-COFECUB (2012-2013) with Porto Alegre University, Brasil
- GDR Singularités (French network on singularities)