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BMO and Injectivity of Space Quasiregular Mappings
Author(s) -
Martio Olli,
Ryazanov Vladimir,
Vuorinen Matti
Publication year - 1999
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.3212050108
Subject(s) - mathematics , norm (philosophy) , bounded mean oscillation , homeomorphism (graph theory) , space (punctuation) , pure mathematics , mathematical analysis , oscillation (cell signaling) , tensor (intrinsic definition) , discrete mathematics , hardy space , computer science , political science , law , operating system , biology , genetics
It is shown that if the dilatation tensor G f of a space quasi regular mapping f belongs to the space VMO (vanishing mean oscillation), then f is a local homeomorphism. The same is true If the BMO‐norm of G f is small or if G f is only close to the VMO space in the BMO‐norm.