Corpus ID: 237491739

The normal growth exponent of a codimension-1 hypersurface of a negatively curved manifold

@inproceedings{Bregman2021TheNG,
  title={The normal growth exponent of a codimension-1 hypersurface of a negatively curved manifold},
  author={Corey J. Bregman and Merlin Incerti-Medici},
  year={2021}
}
Let X be a Hadamard manifold with pinched negative curvature −b ≤ κ ≤ −1. Suppose Σ ⊆ X is a totally geodesic, codimension-1 submanifold and consider the geodesic flow Φνt on X generated by a unit normal vector field ν on Σ. We say the normal growth exponent of Σ in X is at most β if lim t→±∞ ‖dΦνt ‖∞ eβ|t| < ∞, where ‖dΦνt ‖∞ is the supremum of the operator norm of dΦ ν t over all points of Σ. We show that if Σ is bi-Lipschitz to hyperbolic n-space H and the normal growth exponent is at most 1… Expand

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References

SHOWING 1-10 OF 27 REFERENCES
Compact negatively curved manifolds (of dim [unk] 3,4) are topologically rigid.
  • F. Farrell, L. E. Jones
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1989
Let M be a complete (connected) Riemannian manifold having finite volume and whose sectional curvatures lie in the interval [c(1), c(2)] with -infinity < c(1)[unk]c(2) < 0. Then any proper homotopyExpand
The entropy formula for the Ricci flow and its geometric applications
We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometricExpand
A topological analogue of Mostow’s rigidity theorem
Three types of manifolds, spherical, fiat, and hyperbolic, are paradigms of geometric behavior. These are the Riemannian manifolds of constant positive, zero, and negative sectional curvatures,Expand
A boundary criterion for cubulation
We give a criterion in terms of the boundary for the existence of a proper cocompact action of a word-hyperbolic group on a ${\rm CAT}(0)$ cube complex. We describe applications towards lattices andExpand
Ergodic Properties of Geodesic Flows on Closed Riemannian Manifolds of Negative Curvature
Citation in format AMSBIB \Bibitem{Ano67} \by D.~V.~Anosov \paper Geodesic flows on closed Riemannian manifolds of negative curvature \serial Trudy Mat. Inst. Steklov. \yr 1967 \vol 90 \pages 3--210Expand
Systoles of hyperbolic manifolds
We show that for every $n\geq 2$ and any $\epsilon>0$ there exists a compact hyperbolic $n$-manifold with a closed geodesic of length less than $\epsilon$. When $\epsilon$ is sufficiently small theseExpand
Riemannian Geometry
THE recent physical interpretation of intrinsic differential geometry of spaces has stimulated the study of this subject. Riemann proposed the generalisation, to spaces of any order, of Gauss'sExpand
Ricci flow with surgery on three-manifolds
This is a technical paper, which is a continuation of math.DG/0211159. Here we construct Ricci flow with surgeries and verify most of the assertions, made in section 13 of that e-print: theExpand
Pinching constants for hyperbolic manifolds
SummaryWe show in this paper that for everyn≧4 there exists a closedn-dimensional manifoldV which carries a Riemannian metric with negative sectional curvatureK but which admits no metric withExpand
Convex projective structures on Gromov-Thurston manifolds
We consider Gromov–Thurston examples of negatively curved n-manifolds which do not admit metrics of constant sectional curvature. We show that for each n ≥ 4 some of the Gromov–Thurston manifoldsExpand
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