Generalized Yamabe Flows

TL;DR

This paper introduces a broad family of conformal flows extending the classical Yamabe flow, proving long-term existence and convergence in certain cases, with simpler proofs than the classical approach.

Contribution

It generalizes the Yamabe flow, providing new existence and convergence results with simplified proofs for a wider class of flows.

Findings

Long-time existence for a large class of generalized Yamabe flows

Convergence established for negative scalar curvature cases

Simpler proof techniques compared to classical Yamabe flow analysis

Abstract

In this work we introduce a family of conformal flows generalizing the classical Yamabe flow. We prove that for a large class of such flows long-time existence holds, and the arguments are in fact simpler than in the classical case. Moreover, we establish convergence for the case of negative scalar curvature and expect a similar statement for the positive and the flat cases as well.