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math.DG2014★ 6 cited
Smoothing 3-dimensional polyhedral spaces
Nina Lebedeva, Vladimir Matveev, Anton Petrunin +1
We show that 3-dimensional polyhedral manifolds with nonnegative curvature in the sense of Alexandrov can be approximated by nonnegatively curved 3-dimensional Riemannian manifolds…
math.DG2014★ 5 cited
Local characterization of polyhedral spaces
Nina Lebedeva, Anton Petrunin
We show that a compact length space is polyhedral if a small spherical neighborhood of any point is conic.