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Minimal volume invariants, topological sphere theorems and biorthogonal curvature on 4‐manifolds

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  • Ezio Costa
  • Ernani Ribeiro

Abstract

The goal of this article is to establish estimates involving the Yamabe minimal volume, mixed minimal volume and some topological invariants on compact 4‐manifolds. In addition, we provide topological sphere theorems for compact submanifolds of spheres and Euclidean spaces, provided that the full norm of the second fundamental form is suitably bounded.

Suggested Citation

  • Ezio Costa & Ernani Ribeiro, 2019. "Minimal volume invariants, topological sphere theorems and biorthogonal curvature on 4‐manifolds," Mathematische Nachrichten, Wiley Blackwell, vol. 292(3), pages 556-572, March.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:3:p:556-572
    DOI: 10.1002/mana.201700041
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