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...
Courants positifs extrêmaux et conjecture de Hodge.
Courbes pseudo-holomorphes équisingulières en dimension 4
Courbure scalaire et trous noirs
Covariant approach to natural transformations of Weil functors
Covariant Cauchy-Riemann operators and higher Laplacians on Kähler manifolds.
Covariantization of quantized calculi over quantum groups
We introduce a method for construction of a covariant differential calculus over a Hopf algebra from a quantized calculus , , where is a candidate for a Dirac operator for . We recover the method of construction of a bicovariant differential calculus given by T. Brzeziński and S. Majid created from a central element of the dual Hopf algebra . We apply this method to the Dirac operator for the quantum given by S. Majid. We find that the differential calculus obtained by our method is the...
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.
CR mappings and their holomorphic extension
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.
Critère d'exactitude pour les formes de degré 1 sur les quadriques complexes
Critical configurations of planar robot arms
It is known that a closed polygon P is a critical point of the oriented area function if and only if P is a cyclic polygon, that is, P can be inscribed in a circle. Moreover, there is a short formula for the Morse index. Going further in this direction, we extend these results to the case of open polygonal chains, or robot arms. We introduce the notion of the oriented area for an open polygonal chain, prove that critical points are exactly the cyclic configurations with antipodal endpoints and derive...
Critical diffusions
Critical groups computations on a class of Sobolev Banach spaces via Morse index
Critical groups of critical points produced by local linking with applications.
Critical orbits of symmetric functionals.
Critical point theorems.
Critical point theorems on Finsler manifolds.