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 Lie group of real analytic diffeomorphisms is not real analytic
We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense of Milnor. ...
The linking number of singular maps.
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 Index Formula in Noncommutative Geometry.
The local structure of Nodal set of solutions of Schrödinger equation on Riemannian 3-manifolds.
The Logarithm of the Dedekind n-Function.
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 Łojasiewicz gradient inequality in a neighbourhood of the fibre
Some estimates of the Łojasiewicz gradient exponent at infinity near any fibre of a polynomial in two variables are given. An important point in the proofs is a new Charzyński-Kozłowski-Smale estimate of critical values of a polynomial in one variable.
The manifold of Euclidean inner products of sphere.
The marked length spectrum vs. the Laplace spectrum on forms on Riemannian nilmanifolds.
The maximal function of a complex measure
The meaning of time and covariant superderivatives in supermechanics.