Steady States for One Dimensional Conformal Metric Flows

Abstract

We define two conformal structures on $S^1$ which give rise to a different view of the affine curvature flow and a new curvature flow, the ``$Q$-curvature flow". The steady state of these flows are studied. More specifically, we prove four sharp inequalities, which state the existences of the corresponding extremal metrics.

22 pages, typos corrected

References in corpus (1)

• On the higher order conformal covariant operators on the sphere