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June 2020 Differentiable sphere theorems whose comparison spaces are standard spheres or exotic ones
Kei Kondo, Minoru Tanaka
Kodai Math. J. 43(2): 349-365 (June 2020). DOI: 10.2996/kmj/1594313558

Abstract

We show that for an arbitrarily given closed Riemannian manifold $M$ admitting a point $p \in M$ with a single cut point, every closed Riemannian manifold $N$ admitting a point $q \in N$ with a single cut point is diffeomorphic to $M$ if the radial curvatures of $N$ at $q$ are sufficiently close in the sense of $L^1$-norm to those of $M$ at $p$.

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Kei Kondo. Minoru Tanaka. "Differentiable sphere theorems whose comparison spaces are standard spheres or exotic ones." Kodai Math. J. 43 (2) 349 - 365, June 2020. https://doi.org/10.2996/kmj/1594313558

Information

Published: June 2020
First available in Project Euclid: 9 July 2020

zbMATH: 07227754
MathSciNet: MR4121367
Digital Object Identifier: 10.2996/kmj/1594313558

Rights: Copyright © 2020 Tokyo Institute of Technology, Department of Mathematics

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Vol.43 • No. 2 • June 2020
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