Mathematics > Differential Geometry
[Submitted on 15 Jul 2022]
Title:Polyhedral approximations of Riemannian manifolds
View PDFAbstract:We give a condition on the curvature tensors of Riemannian manifolds that admit Lipschitz approximation by polyhedral metrics with curvature bounded below or above.
We show that this condition is also sufficient for the existence of local approximations. We conjecture that it is also sufficient for the global approximations and prove it in some special cases.
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