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)