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

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

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 no...

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Veröffentlicht in:Mathematische Nachrichten 2019-03, Vol.292 (3), p.556-572
Hauptverfasser: Costa, Ezio, Ribeiro, Ernani
Format: Artikel
Sprache:eng
Schlagworte:
4‐manifold
biorthogonal curvature
Control systems
Curvature
Invariants
Manifolds (mathematics)
minimal volume
Pneumatics
Primary: 53C21, 53C23
Secondary: 53C25
sphere theorem
Theorems
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Zusammenfassung: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.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201700041