scholarly journals Degree theorems and Lipschitz simplicial volume for nonpositively curved manifolds of finite volume

2009 ◽  
Vol 2 (1) ◽  
pp. 193-225 ◽  
Author(s):  
Clara Löh ◽  
Roman Sauer
Keyword(s):  
Finite Volume ◽  
Simplicial Volume ◽  
Curved Manifolds ◽  
Nonpositively Curved

scholarly journals Simplicial volume of compact manifolds with amenable boundary

2014 ◽  
Vol 07 (01) ◽  
pp. 23-46 ◽  
Author(s):  
Sungwoon Kim ◽  
Thilo Kuessner
Keyword(s):  
Fundamental Group ◽  
Finite Volume ◽  
Compact Manifold ◽  
Riemannian Metric ◽  
Compact Manifolds ◽  
Simplicial Volume ◽  
Curved Manifolds ◽  
Negatively Curved ◽  
Path Component ◽  
Proportionality Principle

Let M be the interior of a connected, oriented, compact manifold V of dimension at least 2. If each path component of ∂V has amenable fundamental group, then we prove that the simplicial volume of M is equal to the relative simplicial volume of V and also to the geometric (Lipschitz) simplicial volume of any Riemannian metric on M whenever the latter is finite. As an application we establish the proportionality principle for the simplicial volume of complete, pinched negatively curved manifolds of finite volume.

scholarly journals Conjugacy and rigidity for nonpositively curved manifolds of higher rank

Topology ◽  
1996 ◽  
Vol 35 (2) ◽  
pp. 273-286 ◽  
Author(s):  
Christopher B. Croke ◽  
Patrick Eberlein ◽  
Bruce Kleiner
Keyword(s):  
Curved Manifolds ◽  
Nonpositively Curved ◽  
Higher Rank
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