The resolvent expansion for the signature operator on a manifold with a conic singular stratum
The resolvent for Laplace-type operators on asymptotically conic spaces
Let be a compact manifold with boundary, and a scattering metric on , which may be either of short range or “gravitational” long range type. Thus, gives the geometric structure of a complete manifold with an asymptotically conic end. Let be an operator of the form , where is the Laplacian with respect to and is a self-adjoint first order scattering differential operator with coefficients vanishing at and satisfying a “gravitational” condition. We define a symbol calculus for...
The Riemann-Roch theorem for elliptic operators and solvability of elliptic equations with addititonal conditions on compact subsets.
The Riemann-Roch theorem for elliptic operators and solvability of elliptic equations with additional conditions on compact subsets
The role of symmetry and separation in surface evolution and curve shortening.
The Scalar Curvature and the Spectrum of the Laplacian of Spin Manifolds.
The Schrödinger equation on a compact manifold : Strichartz estimates and applications
We prove Strichartz estimates with fractional loss of derivatives for the Schrödinger equation on any riemannian compact manifold. As a consequence we infer global existence results for the Cauchy problem of nonlinear Schrödinger equations on surfaces in the case of defocusing polynomial nonlinearities, and on three-manifolds in the case of quadratic nonlinearities. We also discuss the optimality of these Strichartz estimates on spheres.
The second Yamabe invariant with singularities
Let be a compact Riemannian manifold of dimension .We suppose that is a metric in the Sobolev space with and there exist a point and such that is smooth in the ball . We define the second Yamabe invariant with singularities as the infimum of the second eigenvalue of the singular Yamabe operator over a generalized class of conformal metrics to and of volume . We show that this operator is attained by a generalized metric, we deduce nodal solutions to a Yamabe type equation with...
The second-order Klein-Gordon field equation.
The semiring of immersions of manifolds.
The shallow water equations: Conservation laws and symplectic geometry.
The signature package on Witt spaces
In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of —is well-defined....
The signature theorem for manifolds with metric horns
The spectra and the symmetric structure on a compact symmetric space.
The Spectrum of Fermat Curves.
The Spectrum of Positive Elliptic Operators and Periodic Bicharacteristics.
The spectrum of the -Laplacian on Kähler manifolds
The Spectrum of the Bochner-Laplace Operator on the 1-Forms on a Compact Riemannian Manifold.
The spectrum of the damped wave operator for a bounded domain in .
The spectrum of the Laplace operator for a spherical space form
Si determina lo spettro di un operatore di Laplace di una «spherical space form» e si studia l’influenza di tale spettro su .