27 citations · 78 across the 12 of their papers we have counts for
12 papers
Curvature bounds, regularity and inextendibility of spacetimes
Tobias Beran, John Harvey, Clemens Sämann
We provide a completely new relation between curvature bounds and definiteness of the causal character of maximizers by exploiting the robust notion of synthetic curvature. This en…
A Survey of Dimension Estimation Methods
James A. D. Binnie, Paweł Dłotko, John Harvey +2
It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instance…
A Toponogov globalisation result for Lorentzian length spaces
Tobias Beran, John Harvey, Lewis Napper +1
In the synthetic geometric setting introduced by Kunzinger and Sämann, we present an analogue of Toponogov's Globalisation Theorem which applies to Lorentzian length spaces with lo…
Estimating the reach of a manifold via its convexity defect function
Clément Berenfeld, John Harvey, Marc Hoffmann +1
The reach of a submanifold is a crucial regularity parameter for manifold learning and geometric inference from point clouds. This paper relates the reach of a submanifold to its c…
Almost non-negatively curved 4-manifolds with torus symmetry
John Harvey, Catherine Searle
We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also ad…
Positively curved Riemannian orbifolds and Alexandrov spaces with circle symmetry in dimension 4
John Harvey, Catherine Searle
We classify positively curved Alexandrov spaces of dimension 4 with an isometric circle action up to equivariant homeomorphism, subject to a certain additional condition on the inf…
Semi-free actions with manifold orbit spaces
John Harvey, Martin Kerin, Krishnan Shankar
In this paper, we study smooth, semi-free actions on closed, smooth, simply connected manifolds, such that the orbit space is a smoothable manifold. We show that the only simply co…
Convergence of isometries, with semicontinuity of symmetry of Alexandrov spaces
John Harvey
The equivariant Gromov--Hausdorff convergence of metric spaces is studied. Where all isometry groups under consideration are compact Lie, it is shown that an upper bound on the dim…
Orbifold finiteness under geometric and spectral constraints
John Harvey
The class of Riemannian orbifolds of dimension n defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter has only finitely many member…
Equivariant Alexandrov geometry and orbifold finiteness
John Harvey
Let a compact Lie group act isometrically on a non-collapsing sequence of compact Alexandrov spaces with fixed dimension and uniform lower curvature and upper diameter bounds. If t…
G-actions with close orbit spaces
John Harvey
The classification of G-spaces by Palais is refined for the case where the orbit space satisfies certain mild topological hypotheses. It is shown that when a sequence of such orbit…
Orientation and symmetries of Alexandrov spaces with applications in positive curvature
John Harvey, Catherine Searle
We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact…