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Hyperbolic Rank of Products

Thomas Foertsch·Viktor Schroeder
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Abstract

Generalizing results due to Brady and Farb we prove the existence of a bilipschitz embedded manifold of pinched negative curvature and dimension m_1+m_2-1 in the product X:=X_1^{m_1} times X_2^{m_2} of two Hadamard manifolds X_i^{m_i} of dimension m_i with pinched negative curvature. Combining this result with a Theorem by Buyalo and Schroeder we prove the additivity of the hyperbolic rank for products of manifolds with pinched negative curvature.

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Thomas Foertsch, Viktor Schroeder. 2002-08-26. Hyperbolic Rank of Products. https://arxiv.org/abs/math/0208197

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