A bumpy metric theorem and the Poisson relation for generic strictly convex domains.
About a decomposition of the space of symmetric tensors of compact support on a Riemann manifold.
Convergence of Riemannian manifolds and Laplace operators. I
We study the spectral convergence of compact Riemannian manifolds in relation with the Gromov-Hausdorff distance and discuss the geodesic distances and the energy forms of the limit spaces.
Convexity on the space of Kähler metrics
These are the lecture notes of a minicourse given at a winter school in Marseille 2011. The aim of the course was to give an introduction to recent work on the geometry of the space of Kähler metrics associated to an ample line bundle. The emphasis of the course was the role of convexity, both as a motivating example and as a tool.
Dirac and Plateau billiards in domains with corners
Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C 2-smooth Riemannian metrics g on a smooth manifold X, such that scalg(x) ≥ κ(x), is closed under C 0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry,...
Einstein Metrics and Complex Structures.
Finiteness of and geometric inequalities in almost positive Ricci curvature
Group actions, gauge transformations, and the calculus of variations.
Heterogeneous Riemannian manifolds.
Les travaux de Nabutovsky et Weinberger sur la complexité de l'espace des variétés riemanniennes
Les variétés hyperboliques sont des minima locaux de l'entropie topologique.
Moduli of half conformally flat structures.
Normal Families and the Semicontinuity of Isometry and Automorphism Groups.
On a Purely ?Riemannian" Proof of the Structure and Dimension of the Unramified Moduli Space of a Compact Riemann Surface.
On an energy function for the Weil-Petersson metric on Teichmüller space.
On the creation of conjugate points.
On the relation between the Einstein and the Komar expressions for the energy of the gravitational field
On the space of asymptotically euclidean metrics
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite riemannian metric
For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian exponential...
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric
For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential...