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Shu-Cheng Chang

2011-10-13
15:00:00 - 16:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

The study of Hamilton's Ricci flow has been dominated by the maximum principle with an exception to Hamilton's entropy estimate which holds for closed surfaces with positive Gaussian curvature. Then it is very interesting to find entropy formulae for integrals of local geometric quantities. An exciting recent example is the Perelman's entropy functional. Its monotonicity property of the entropy functional together with Li-Yau-Perelman reduced distance imply the no local collapsing theorem under the Ricci flow. In this talk, we derive the CR analogue of Perelman's Harnack estimate for the positive solution of the CR conjugate heat equation under the CR curvature flows. As consequences, we obtain monotonicity properties of CR Perelman F-entropy and W-functional and provide a classification of the CR solitons. At the end, we are able to show the asymptotic convergence for the solution of CR Yamabe flow in a closed spherical CR 3-manifold with positive Tanaka-Webster curvature and vanishing torsion.