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math.DG2024
Veronese minimizes normal curvatures
Anton Petrunin
Suppose M is a closed submanifold in a Euclidean ball of sufficiently large dimension. We give an optimal bound on the normal curvatures, guaranteeing that M is a sphere. The borde…
math.DG2024
Tubed embeddings
Anton Petrunin
We consider the following question: When does a Riemannian manifold admit an embedding with a uniformly thick tubular neighborhood in another Riemannian manifold of large dimension…