Related papers: Ruelle and Quantum Resonances for Open Hyperbolic …
We compute the Laplacian spectra of singular area-minimising hypersurfaces in the hyperbolic space with prescribed asymptotic data. We also obtain similar results in higher codimension, and explore related extremal properties of the bottom…
We calculate the Euler characteristic of associated vector bundles over the moduli spaces of stable parabolic bundles on smooth curves. Our method is based on a wall-crossing technique from Geometric Invariant Theory, certain iterated…
Quantum channels describe subsystem or open system evolution. Using the classical Koopman operator that evolves functions on phase space, 4 classical Koopman channels are identified that are analogs of the 4 possible quantum channels in a…
We give a lower bound for the bottom of the $L^2$ differential form spectrum on hyperbolic manifolds, generalizing thus a well-known result due to Sullivan and Corlette in the function case. Our method is based on the study of the resolvent…
Given a filling primitive geodesic curve in a closed hyperbolic surface one obtains a hyperbolic three-manifold as the complement of the curve's canonical lift to the projective tangent bundle. In this paper we give the first known lower…
The correspondence principle bridges the quantum and classical worlds by establishing a direct link between their dynamics. This well-accepted tenant of quantum physics has been explored in quantum systems wherein the number of particles is…
The space forms, the complex hyperbolic spaces and the quaternionic hyperbolic spaces are characterized as the harmonic manifolds with specific radial eigenfunctions of the Laplacian.
For a fixed word hyperbolic group we compare different residual properties related to quasiconvex subgroups.
We consider a nonlinear optical system in general, and a broad aperture laser in particular in a resonator where the diffraction coefficients are of opposite signs along two transverse directions. The system is described by the hyperbolic…
The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…
Motivated by the moduli theory of taut contact circles on spherical 3-manifolds, we relate taut contact circles to transversely holomorphic flows. We give an elementary survey of such 1-dimensional foliations from a topological viewpoint.…
Let $M$ be a closed, negatively curved Riemannian manifold of dimension $n \neq 4, 8$ with strictly $1/4$-pinched sectional curvature. We prove, that if the frame flow is ergodic and the sum of its unstable and stable bundles together with…
Motivated by spectral asymptotics for orbital integrals in a relative trace formula, we generalize a number of geometric properties of geodesics in the hyperbolic plane, to maximal flat submanifolds of symmetric spaces of non-compact type.
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We introduce a natural subset of the unit tangent bundle of a convex projective manifold, the biproximal unit tangent bundle; it is closed and invariant under the geodesic flow, and we prove that the geodesic flow is topologically mixing on…
In this paper, a correspondence via duality is established between the set of locally strongly convex symmetric equiaffine hyperspheres and the set of minimal symmetric Lagrangian submanifolds in a certain complex space form. By using this…
Mean curvature flows of isoparametric submanifolds in Euclidean spaces and spheres have been studied by Liu and Terng. In particular, it was proved that such flows always have ancient solutions. This is also true for mean curvature flows of…
We construct a global hypersurface of section for the geodesic flow of a convex hypersurface in Euclidean space admits an isometric involution. This generalizes the Birkhoff annulus to higher dimensions.
We study topological phases in the hyperbolic plane using noncommutative geometry and T-duality, and show that fractional versions of the quantised indices for integer, spin and anomalous quantum Hall effects can result. Generalising models…
It is shown that any second order dynamic equation on a configuration bundle $Q\to R$ of non-relativistic mechanics is equivalent to a geodesic equation with respect to a (non-linear) connection on the tangent bundle $TQ\to Q$. The case of…