Convergence of the Yamabe flow for arbitrary initial energy. (English) Zbl 1085.53028

Brendle, Simon

J. Differ. Geom. 69, No. 2, 217-278 (2005).

A general convergence result for the Yamabe flow in conformal geometry is presented. It is worth to stress that the convergence is proved for arbitrary initial energy. Important related geometric aspects and developments are pointed out.

Reviewer: Dumitru Motreanu (Perpignan)

MSC:

53C21	Methods of global Riemannian geometry, including PDE methods; curvature restrictions
35K55	Nonlinear parabolic equations
53C44	Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)

Keywords:

Yamabe flow; Riemannian metric; curvature; evolution equation