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Hyperbolic rank of products

Authors:	Thomas Foertsch Viktor Schroeder

Institution:	Universität Zürich, Mathematisches Institut, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland ; Universität Zürich, Mathematisches Institut, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

Abstract:	Generalizing a result of Brady and Farb (1998), we prove the existence of a bilipschitz embedded manifold of negative curvature bounded away from zero and dimension in the product $X:=X_1^{m_1}\times X_2^{m_2}$ of two Hadamard manifolds $X_i^{m_i}$ of dimension with negative curvature bounded away from zero. Combining this result with a result of Buyalo and Schroeder (2002), we prove the additivity of the hyperbolic rank for products of manifolds with negative curvature bounded away from zero.

Keywords:	Hadamard manifolds hyperbolic rank

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