Convexity at infinity and Brownian motion on manifolds with unbounded negative curvature.
Convexity for invariant differential operators on semisimple symmetric spaces
Corner Mellin operators and conormal asymptotics
Corner Mellin operators and reduction of orders with parameters
Correction : “On two transfer principles in stochastic differential geometry”
Correction to : “On isospectral deformations of riemannian metrics. II”
Correction to "On the characterization of flat metrics by the spectrum"
Correction to “Properties of pseudoholomorphic curves in symplectisations. I : asymptotics”
Correction to: Spectral Geometry and the Kaehler Condition for Complex Manifolds.
Correction to "Uniqueness for the harmonic map flow from surfaces to general targets".
Corrigendum to: Asymptotic expansion in time of the Schrödinger group on conical manifolds
We correct an error in the normalizing constant of resonant states.
Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary
In this paper we consider a smooth and bounded domain of dimension with boundary and we construct sequences of solutions to the wave equation with Dirichlet boundary condition which contradict the Strichartz estimates of the free space, providing losses of derivatives at least for a subset of the usual range of indices. This is due to microlocal phenomena such as caustics generated in arbitrarily small time near the boundary. Moreover, the result holds for microlocally strictly convex domains...
Covariant Cauchy-Riemann operators and higher Laplacians on Kähler manifolds.
Covering lemmas and BMO estimates for eigenfunctions on Riemannian surfaces.
The principal aim of this note is to prove a covering Lemma in R2. As an application of this covering lemma, we can prove the BMO estimates for eigenfunctions on two-dimensional Riemannian manifolds (M2, g). We will get the upper bound estimate for || log |u| ||BMO, where u is the solution to Δu + λu = 0, for λ > 1 and Δ is the Laplacian on (M2, g). A covering lemma on homogeneous spaces is also obtained in this note.
Coverings, heat kernels and spanning trees.
Cramér's formula for Heisenberg manifolds
Let be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that , where is a specific nonzero constant and is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the -dimensional case.
Critical diffusions
Critical points at infinity in the variational calculus
Critical points of the steady state of a Fokker-Planck equation.
Crochet de Jacobi non local sur un revêtement et ses applications à l’étude de l’équation de Burgers