most recent 30 from http://mathoverflow.net 2013-06-19T06:50:46Z http://mathoverflow.net/feeds/question/101146 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/101146/short-time-existence-on-hyperbolic-ricci-flow-in-non-compact-case Hassan Jolany 2012-07-02T14:19:45Z 2013-04-15T23:10:40Z

<p>We know</p> <ul> <li>Laplace equation (elliptic equations) $ Δ u = 0$</li> <li>Heat equation (parabolic equations) $u_t − Δu = 0$</li> <li>Wave equation (hyperbolic equations) $u_{tt} − Δu = 0$</li> </ul> <p>we have - Hyperbolic geometric flow (hyperbolic equations)</p> <p>$\frac{∂^2}{∂t^2}g_{ij}(t)=-2R_{ij}$</p> <p>Do any body know the short time existence for heat equation <strong>Hyperbolic Ricci flow</strong>, when our Manifold is non-compact? </p> <p>and second question: Hyperbolic Ricci flow is invariant under first Chern class?</p>