Abstract

We consider the Cauchy problem for hyperbolic geometric flow equations introduced recently by Kong and Liu motivated by the Einstein equation and Hamilton Ricci flow, and obtain a necessary and sufficient condition for the global existence of classical solutions to this kind of flow on Riemann surfaces. The results show that the scalar curvature of the solution metric g ij converges to one of flat curvature, and the hyperbolic geometric flow has the advantage that the surgery technique may be replaced by choosing a suitable initial velocity tensor.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.