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Boundary of Anosov dynamics and evolution equations for surfaces
Author(s) -
Jane Dan,
Ruggiero Rafael O.
Publication year - 2014
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.201300259
Subject(s) - mathematics , ricci flow , flow (mathematics) , curvature , genus , closure (psychology) , boundary (topology) , surface (topology) , pure mathematics , mathematical analysis , ricci curvature , geometry , botany , biology , economics , market economy
We show that a C ∞ compact surface of genus greater than one, without focal points and a finite number of bubbles (“good” shaped regions of positive curvature) is in the closure of Anosov metrics. Compact surfaces of nonpositive curvature and genus greater than one are in the closure of Anosov metrics, by Hamilton's work about the Ricci flow. We generalize this fact to the above surfaces without focal points admitting regions of positive curvature using a “magnetic” version of the Ricci flow, the so‐called Ricci Yang‐Mills flow.