Degree theorems and Lipschitz simplicial volume for nonpositively curved manifolds of finite volume
By Clara Loeh, Roman Sauer. 2007
48 citations recorded by the source corpus.
We study a metric version of the simplicial volume on Riemannian manifolds, the Lipschitz simplicial volume, with applications to degree theorems in mind. We establish a proportionality principle and a product inequality from which we derive an extension of Gromov's volume comparison theorem to products of negatively curved manifolds or locally symmetric spaces of noncompact type. In contrast, we provide vanishing results for the ordinary simplicial volume; for instance, we show that the ordinary simplicial volume of noncompact locally symmetric spaces with finite volume of ℚ‐rank at least 3 is zero.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9f506955de912c7b4ef1f67aec86ec796ad0c11a
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Geodesic finite elements on simplicial grids (2012, background): “2 The desirability of this simple invariance forces us to disregard an alternative interpolation method that appears in [19].”