# 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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