Positive pinching, volume and second Betti number

Fuquan Fang, Xiaochun Rong

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Our main theorem asserts that for all odd n ≥ 3 and 0 < δ ≤ 1, there exists a small constant, i(n, δ) > 0, such that if a simply connected n-manifold, M, with vanishing second Betti number admits a metric of sectional curvature, δ ≤ KM ≤ 1, then the injectivity radius of M is greater than i(n, δ).

Original languageEnglish (US)
Pages (from-to)641-674
Number of pages34
JournalGeometric and Functional Analysis
Issue number4
StatePublished - 1999

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


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