141 citations · 555 across the 57 of their papers we have counts for
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math.DG2022★ 12 cited
Polyhedral approximations of Riemannian manifolds
Anton Petrunin
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 th…
math.DG2022★ 6 cited
Curvature tensor of smoothable Alexandrov spaces
Nina Lebedeva, Anton Petrunin
We prove weak convergence of curvature tensors of Riemannian manifolds for converging noncollapsing sequences with a lower bound on sectional curvature.
math.DG2022★ 1 cited
Five-point Toponogov theorem
Nina Lebedeva, Anton Petrunin
We give an if-and-only-if condition on a five-point metric spaces that admit embeddings into nonnegatively curved Riemannian manifolds.