Polyhedral approximations of Riemannian manifolds

Authors : Anton Petrunin

Pages : 173-188

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Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :I'm trying to understand which Riemannian manifolds can be Lipschitz approximated by polyhedral spaces of the same dimension with curvature bounded below. The necessary conditions I found consist of some special inequality for curvature at each point (the geometric curvature bound). This inequality is also sufficient condition for local approximation. I conjecture that it is also a sufficient condition for global approximation, and I can prove it if the curvature bound is positive. In general I can prove it only with the additional assumption that tangent bundle of the manifold is stably trivial.
Keywords : Turk. J. Math., 27, (2003), 173-188. Full text: pdf Other articles published in the same issue: Turk. J. Math., vol.27, iss.1.