The numerical integration of the Schr\"odinger equation by discretization time is explored for curved manifolds arising from finite representations based on evolving basis states. In particular, unitarity evolution assessed, in sense conservation mutual scalar products a set states, and with them orthonormality particle number. Although adequately represented known to give rise unitary spite cu...

In this note, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into L1. As a corollary, we obtain that all planar graphs which are 1skeletons of planar non-positively curved complexes with regular Euclidean polygons as cells are L1-embeddable with distortion at most 2 + π/2 < 4. Our results significantly improve and simplify the...

If a class of finitely generated groups G is closed under isometric amalgamations along free subgroups, then every G ∈ G can be quasi-isometrically embedded in a group Ĝ ∈ G that has no proper subgroups of finite index. Every compact, connected, non-positively curved space X admits an isometric embedding into a compact, connected, non-positively curved space X such that X has no non-trivial fin...

We completely characterize the sectional curvature of all 13-dimensional Bazaikin spaces. In particular, we show that spaces admit a quasi-positively curved Riemannian metric, and that, up to isometry, there is unique space which almost positively but not curved.

This paper explores the relation between structure of fibre bundles akin to those associated a closed almost nonnegatively sectionally curved manifold and rational homotopy theory.

This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisely, we show they have finite telescopic dimension. We also show the existence of Furstenberg maps for some group actions on these spaces. Such maps appear as a first step toward superrigidity results.

Title of dissertation: LENGTH SPECTRAL RIGIDITY OF NON-POSITIVELY CURVED SURFACES Jeffrey Frazier, Doctor of Philosophy, 2012 Dissertation directed by: Professor William Goldman Department of Mathematics Length spectral rigidity is the question of under what circumstances the geometry of a surface can be determined, up to isotopy, by knowing only the lengths of its closed geodesics. It is known...