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Creators/Authors contains: "Petrunin, Anton"

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  1. ; (, Journal of Topology and Analysis)
    We show that metric trees and their products meet the octahedron comparison, which is a certain six-point metric comparison similar to Alexandrov’s CAT(0) comparison. 
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    Free, publicly-accessible full text available October 1, 2026
  2. ; (, The American Mathematical Monthly)
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  3. (, Geometric and Functional Analysis)
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  4. ; (, Geometry & Topology)
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  5. ; (, Israel Journal of Mathematics)
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  6. ; (, International Mathematics Research Notices)
    We give an if-and-only-if condition on five-point metric spaces that admit isometric embeddings into complete nonnegatively curved Riemannian manifolds. 
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  7. ; (, Journal of Optimization Theory and Applications)
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  8. ; ; (, The American Mathematical Monthly)
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  9. (, The Mathematical Intelligencer)
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  10. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract We give a necessary condition on a geodesic in a Riemannian manifold that can run in some convex hypersurface.As a corollary, we obtain peculiar properties that hold true for every convex set in any generic Riemannian manifold ( M , g ) {(M,g)} .For example, if a convex set in ( M , g ) {(M,g)} is bounded by a smooth hypersurface, then it is strictly convex. 
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