A note on pinching sphere theorem.
type: Item
instance of: scholarly article
title: A note on pinching sphere theorem.
zbMATH Open document ID: 1046.53019
author: Yuliang Wen
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2004-03-15T00:00:00Z
review text: The main result reads: For any \(n\in\mathbb N\) there exists \(\eta\in \mathbb{R}\) depending only on \(n\) and such that any closed, simply connected \((2n)\)-dimensional Riemannian manifold \(M\) with sectional curvature \(K_M\in (0, 1]\) and volume \(V(M)\in [(3/2)V(S^{2n}), ((3/2)+\eta)V(S^{2n})]\) is homeomorphic to the sphere \(S^{2n}\). The author claims that the proof of a stronger result in [\textit{B. Wang}, J. Sichuan Univ., Nat. Sci. Ed. 34, No. 5, 581--587 (1997; Zbl 0907.53028)] contains a gap.
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 2057092
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: pinching
zbMATH Keywords: sphere
reviewed by: Paweł Walczak
MaRDI profile type: Publication
full work available at URL: j.crma.2003.12.007
OpenAlex ID: W2030920825
cites work: Q4067705
cites work: A Sphere Theorem for Reverse Volume Pinching on Even-Dimensional Manifolds
cites work: Riemannian geometry
cites work: A generalized sphere theorem
cites work: A Sphere Theorem for Manifolds of Positive Ricci Curvature
cites work: Q4384652
DOI: 10.1016/J.CRMA.2003.12.007
description: scientific article; zbMATH DE number 2057092