Skip to main content
Open Access Publications from the University of California

UC Santa Cruz

UC Santa Cruz Previously Published Works bannerUC Santa Cruz

A note on conformal Ricci flow


In this note we study the conformal Ricci flow that Arthur Fischer introduced in 2004. We use DeTurck's trick to rewrite the conformal Ricci flow as a strong parabolic-elliptic partial differential equation. Then we prove short-time existence for the conformal Ricci flow on compact manifolds as well as on asymptotically flat manifolds. We show that the Yamabe constant is monotonically increasing along conformal Ricci flow on compact manifolds. We also show that the conformal Ricci flow is the gradient flow for the ADM mass on asymptotically flat manifolds. © 2014 Mathematical Sciences Publishers.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View