Convergence of the fractional Yamabe flow for a class of initial data

Abstract

This work is a follow-up on the work of the second author with P. Daskalopoulos and J.L. Vázquez. In this latter work, we introduced the Yamabe flow associated to the so-called fractional curvature and prove some existence result of mild (semi-group) solutions. In the present work, we continue this study by proving that for some class of data one can prove actually convergence of the flow in a more general context. We build on the approach simplified in the book of M. Struwe.

References in corpus (3)

• Fractional Laplacians on domains, a development of Hörmander's theory of mu-transmission pseudodifferential operators
• Convergence of scalar-flat metrics on manifolds with boundary under a Yamabe-type flow
• Weak and smooth solutions for a fractional Yamabe flow: the case of general compact and locally conformally flat manifolds

Cited by in corpus (2)

• Multiplicity of singular solutions to the fractional Yamabe problem on spheres
• A fractional conformal curvature flow on the unit sphere