English

A Note on Conformal Ricci Flow

Differential Geometry 2011-09-27 v1

Abstract

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

Keywords

Cite

@article{arxiv.1109.5377,
  title  = {A Note on Conformal Ricci Flow},
  author = {Peng Lu and Jie Qing and Yu Zheng},
  journal= {arXiv preprint arXiv:1109.5377},
  year   = {2011}
}

Comments

22 pages, no figures

R2 v1 2026-06-21T19:09:56.868Z