Perelman’s \(W\)-functional on manifolds with conical singularities. (English) Zbl 1464.53112
Summary: In this paper, we develop the theory of Perelman’s \(W\)-functional on manifolds with isolated conical singularities. In particular, we show that the infimum of \(W\)-functional over a certain weighted Sobolev space on manifolds with isolated conical singularities is finite, and the minimizer exists, if the scalar curvature satisfies certain condition near the singularities. We also obtain an asymptotic order for the minimizer near the singularities.
MSC:
53E20 | Ricci flows |
53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |