Steady States for One Dimensional Conformal Metric Flows
Yilong Ni, Meijun Zhu
Abstract
We define two conformal structures on S1 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.
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