The Index of Manifolds with Toral Actions and Geometric Interpretations of the ... (..., (S1, Mn)) Invariant of Atiyah and Singer.
The index of projective families of elliptic operators.
The index of signature operators on Lipschitz manifolds
The index of transversally elliptic complexes
The infinite Brownian loop on a symmetric space.
The Kashiwara cojugation and wave-front sets of regular holonomic distributions on a complex manifold.
The Kashiwara conjugation and wave-front sets of regular holonomic distributions on a complex manifold (Erratum).
The Laplace operator on a hyperbolic manifold. II. Eisenstein series and the scattering matrix.
The Laplace operator on hyperbolic three manifolds with cusps of non-maximal rank.
The Laplace spectrum and Hermitian spaces.
The Laplace-Beltrami operator in almost-Riemannian Geometry
We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable surfaces for which a local orthonormal frame is given by a pair of vector fields that can become collinear.Under the assumption that the structure is 2-step Lie bracket generating, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence, a quantum particle cannot cross the singular set (i.e., the set where the vector fields become collinear) and the...
The laplacian on asymptotically flat manifolds and the specification of scalar curvature
The large sieve in Riemann surfaces
The length spectrum of riemannian two-step nilmanifolds
The Lenz shift and wiener sausage in riemannian manifolds
The Leray measure of nodal sets for random eigenfunctions on the torus
We study nodal sets for typical eigenfunctions of the Laplacian on the standard torus in dimensions. Making use of the multiplicities in the spectrum of the Laplacian, we put a Gaussian measure on the eigenspaces and use it to average over the eigenspace. We consider a sequence of eigenvalues with growing multiplicity .The quantity that we study is the Leray, or microcanonical, measure of the nodal set. We show that the expected value of the Leray measure of an eigenfunction is constant, equal...
The Lie derivative and cohomology of -structures.
The local index density of the perturbed de Rham complex
A perturbation of the de Rham complex was introduced by Witten for an exact 1-form and later extended by Novikov for a closed 1-form on a Riemannian manifold . We use invariance theory to show that the perturbed index density is independent of ; this result was established previously by J. A. Álvarez López, Y. A. Kordyukov and E. Leichtnam (2020) using other methods. We also show the higher order heat trace asymptotics of the perturbed de Rham complex exhibit nontrivial dependence on . We establish...
The local structure of Nodal set of solutions of Schrödinger equation on Riemannian 3-manifolds.
The Logarithm of the Dedekind n-Function.