Yamabe flow with prescribed scalar curvature

Inas Amacha and Rachid Regbaoui

Vol. 297 (2018), No. 2, 257–275

DOI: 10.2140/pjm.2018.297.257

Abstract

We study the Yamabe flow corresponding to the prescribed scalar curvature problem on compact Riemannian manifolds with negative scalar curvature. The long time existence and convergence of the flow are proved under appropriate conditions on the prescribed scalar curvature function.

Keywords

conformal metric, scalar curvature, Yamabe flow

Mathematical Subject Classification 2010

Primary: 35K55, 53A30, 58J35

Milestones

Received: 22 May 2017

Revised: 26 April 2018

Accepted: 29 April 2018

Published: 20 December 2018