Convergence of compact Ricci solitons

Abstract

We show that sequences of compact gradient Ricci solitons converge to complete orbifold gradient solitons, assuming constraints on volume, the $L^{n/2}$-norm of curvature, and the auxiliary constant $C_1$. The strongest results are in dimension 4, where $L^2$ curvature bounds are equivalent to upper bounds on the Euler number. We obtain necessary and sufficient conditions for limits to be compact.

References in corpus (6)

• Gaussian densities and stability for some Ricci solitons
• Bach-flat asymptotically locally Euclidean metrics
• Compactness theorems of gradient Ricci solitons
• Noncompact Shrinking 4-Solitons with Nonnegative Curvature
• Gradient Kähler-Ricci Solitons and Periodic Orbits
• Complete gradient shrinking Ricci solitons have finite topological type