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Minimal volume invariants, topological sphere theorems and biorthogonal curvature on 4‐manifolds
Author(s) -
Costa Ezio,
Ribeiro Ernani
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700041
Subject(s) - mathematics , biorthogonal system , pure mathematics , bounded function , norm (philosophy) , ricci flat manifold , euclidean geometry , spheres , topology (electrical circuits) , curvature , mathematical analysis , scalar curvature , combinatorics , geometry , physics , wavelet transform , astronomy , artificial intelligence , computer science , political science , wavelet , law
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.