Steady States for One Dimensional Conformal Metric Flows

Details Steady States for One Dimensional Conformal Metric Flows Steady States for One Dimensional Conformal Metric Flows

2006-11-09

arxiv.org/abs/math/0611254v2

Mathematics

Analysis of PDEs

22 pages, typos corrected

Scientific paper

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.

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