Boundary of Anosov dynamics and evolution equations for surfaces |
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| Authors: | Dan Jane Rafael O Ruggiero |
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| Affiliation: | Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, , Rio de Janeiro, 22453‐900 RJ, Brazil |
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| Abstract: | We show that a  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. |
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| Keywords: | Anosov metric focal points Ricci flow geodesic flow conformal deformation of metrics Primary: 37D40 Secondary: 53C44 37D20 |
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