Convergence of the Yamabe flow for arbitrary initial energy

On a classification of the quasi Yamabe gradient solitons

“…Let (M n , g) be an n-dimensional Riemannian manifold with n ≥ 3. If there exists a smooth function f on M n and a constant ρ such that For the study of the Yamabe flow in the compact case, see [12,2,1,20,14,19] and the references therein. It is very important for understanding the singularity formation in the complete Yamabe flow to study the classification of Yamabe solitons.…”

On the geometric flows solving Kählerian inverseσkequations

“…Andrews [1994;2007] studies the curvature flow of embedded convex hypersurfaces in the Euclidean space. Several authors study the σ k -equation in conformal geometry; see, for example, [Viaclovsky 2000;Chang et al 2002;Guan and Wang 2003;Brendle 2005] and references therein. It is thus interesting to explore the corresponding problem in Kähler geometry.…”

Conformal Geometry and Fully Nonlinear Equations

“…Schwetlick and Struwe [SS03] proved convergence for 3 ≤ n ≤ 5 provided an certain energy bound on the initial metric is satsified. In the beautiful paper [Bre05], Simon Brendle proved convergence for 3 ≤ n ≤ 5 for any initial data.…”