English

Polyhedral approximations of Riemannian manifolds

Differential Geometry 2022-07-18 v1 Metric Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.2207.07559,
  title  = {Polyhedral approximations of Riemannian manifolds},
  author = {Anton Petrunin},
  journal= {arXiv preprint arXiv:2207.07559},
  year   = {2022}
}

Comments

an old paper with minor updates