Hyperbolic Rank of Products
نویسندگان
چکیده
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 m1 +m2 − 1 in the product X := X1 1 ×X m2 2 of two Hadamard manifolds Xi i of dimension mi 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.
منابع مشابه
ar X iv : m at h / 02 08 19 7 v 1 [ m at h . D G ] 2 6 A ug 2 00 2 Hyperbolic Rank of Products
Generalizing [BrFa] we prove the existence of a bilipschitz embedded manifold of pinched negative curvature and dimension m1 +m2 −1 in the product X := Xm1 1 ×X m2 2 of two Hadamard manifolds Xmi i of dimension mi with pinched negative curvature. Combining this result with [BuySch] we prove the additivity of the hyperbolic rank for products of manifolds with pinched negative curvature.
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