Evolution of Yamabe constant under Ricci flow
نویسندگان
چکیده
In this note under a crucial technical assumption we derive a differential equality of Yamabe constant Y (g (t)) where g (t) is a solution of the Ricci flow on a closed n-manifold. As an application we show that when g (0) is a Yamabe metric at time t = 0 and Rgα n−1 is not a positive eigenvalue of the Laplacian ∆gα for any Yamabe metric gα in the conformal class [g0], then d dt ∣∣ t=0 Y (g (t)) ≥ 0. Here Rgα is the scalar curvature of gα. Recall that the Yamabe constant of a smooth metric g on closed manifold M is defined by
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