The logarithmic gradient of the kernel of the heat equation with drift on a Riemannian manifold.
The Logarithmic Hardy-Littlewood-Sobolev Inequlity and Extremals of Zeta Functions on Sn.
The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian
This paper discusses the question whether the discrete spectrum of the Laplace-Beltrami operator is infinite or finite. The borderline-behavior of the curvatures for this problem will be completely determined.
The marked length spectrum vs. the Laplace spectrum on forms on Riemannian nilmanifolds.
The micro-support of the complex defined by a convolution operator in tube domains
The normal symbol on Riemannian manifolds.
The Novikov conjecture for linear groups
Let K be a field. We show that every countable subgroup of GL(n,K) is uniformly embeddable in a Hilbert space. This implies that Novikov’s higher signature conjecture holds for these groups. We also show that every countable subgroup of GL(2,K) admits a proper, affine isometric action on a Hilbert space. This implies that the Baum-Connes conjecture holds for these groups. Finally, we show that every subgroup of GL(n,K) is exact, in the sense of C*-algebra theory.
The Paneitz equation in hyperbolic space
The Poincaré-Lelong equation on complete Kähler manifolds
The Poisson boundary for rank one manifolds and their compact lattices.
The positive mass theorem for ALE manifolds
We show what extra condition is necessary to be able to use the positive mass argument of Witten [12] on an asymptotically locally euclidean manifold. Specifically we show that the 'generalized positive action conjecture' holds if one assumes that the signature of the manifold has the correct value.
The proof of the Nirenberg-Treves conjecture
We prove the Nirenberg-Treves conjecture : that for principal type pseudo-differential operators local solvability is equivalent to condition (). This condition rules out certain sign changes of the imaginary part of the principal symbol along the bicharacteristics of the real part. We obtain local solvability by proving a localizable estimate for the adjoint operator with a loss of two derivatives (compared with the elliptic case). The proof involves a new metric in the Weyl (or Beals-Fefferman)...
The propagation of polarization in double refraction
The Propagation of Singularities along Gliding Rays.
The p-spectrum of the Laplacian on compact hyperbolic three manifolds.
The Quantum Birkhoff Normal Form and Spectral Asymptotics
In this talk we explain a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate potential well, yielding uniform estimates in the energy . This permits a detailed study of the spectrum in various asymptotic regions of the parameters , and gives improvements and new proofs for many of the results in the field. In the completely resonant...
The radiation field is a Fourier integral operator
We show that the ``radiation field'' introduced by F.G. Friedlander, mapping Cauchy data for the wave equation to the rescaled asymptotic behavior of the wave, is a Fourier integral operator on any non-trapping asymptotically hyperbolic or asymptotically conic manifold. The underlying canonical relation is associated to a ``sojourn time'' or ``Busemann function'' for geodesics. As a consequence we obtain some information about the high frequency behavior of the scattering...
The reconstruction theorem
The regularity of convolution and restriction of distributions
The Residue of the Local Eta Function at the Origin.