Invariants of characteristics of some systems of partial differential equations.
Inverse Scattering for Waveguides
We study the inverse scattering problem for a waveguide with cylindrical ends, , where each has a product type metric. We prove, that the physical scattering matrix, measured on just one of these ends, determines up to an isometry.
Inverse spectral results on even dimensional tori
Given a Hermitian line bundle over a flat torus , a connection on , and a function on , one associates a Schrödinger operator acting on sections of ; its spectrum is denoted . Motivated by work of V. Guillemin in dimension two, we consider line bundles over tori of arbitrary even dimension with “translation invariant” connections , and we address the extent to which the spectrum determines the potential . With a genericity condition, we show that if the connection is invariant under...
Involutive distributions, invariant manifolds, and defining equations.
Involutive formulation and simulation for electroneutral microfluids
We study a microfluidic flow model where the movement of several charged species is coupled with electric field and the motion of ambient fluid. The main numerical difficulty in this model is the net charge neutrality assumption which makes the system essentially overdetermined. Hence we propose to use the involutive and the associated augmented form of the system in numerical computations. Numerical experiments on electrophoresis and stacking show that the completed system significantly improves...
Involutive formulation and simulation for electroneutral microfluids
We study a microfluidic flow model where the movement of several charged species is coupled with electric field and the motion of ambient fluid. The main numerical difficulty in this model is the net charge neutrality assumption which makes the system essentially overdetermined. Hence we propose to use the involutive and the associated augmented form of the system in numerical computations. Numerical experiments on electrophoresis and stacking show that the completed system significantly improves...
Involutivity of truncated microsupports
Using a result of J.-M. Bony, we prove the weak involutivity of truncated microsupports. More precisely, given a sheaf on a real manifold and , if two functions vanish on , then so does their Poisson bracket.
Isomorphismes entre algèbres d'opérateurs pseudo-différentiels
Isoperimetric constants and the first eigenvalue of a compact riemannian manifold
Isoperimetric Constants of Manifolds with Small Handles.
Isoperimetric profile and uniqueness for Neumann problems
Isospectral Connections on Line Bundles.
Isospectral deformations of closed riemannian manifolds with different scalar curvature
We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on , where is a torus of dimension and is a sphere of dimension . These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.
Isospectral deformations of the Lagrangian Grassmannians
We study the special Lagrangian Grassmannian , with , and its reduced space, the reduced Lagrangian Grassmannian . The latter is an irreducible symmetric space of rank and is the quotient of the Grassmannian under the action of a cyclic group of isometries of order . The main result of this paper asserts that the symmetric space possesses non-trivial infinitesimal isospectral deformations. Thus we obtain the first example of an irreducible symmetric space of arbitrary rank , which is...
Isospectral deformations on Riemannian manifolds which are diffeomorphic to compact Heisenberg manifolds.
Isospectral flat 3-manifolds.
Isospectral flat orientable 2-orbifolds.
Isospectral graphs and isospectral surfaces
Isospectral hyperbolic surfaces have matching geodesics.
Isospectral plane domains and surfaces via Riemannian orbifolds.