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- W2184382450 abstract "Recognizing the deflciency that C. Guenther's arguments can not solve the stability of Ricci ∞ows because of the Ricci ∞ow equation being not strictly parabolic, our previous paper flrst studied the stability of Ricci ∞ows based on Killing conditions. In this paper, we consider the stability of Ricci ∞ows, and of quasi-Ricci ∞ows based on bounded curvature conditions, and also obtain some interesting results. @ @t g = i2Rc(g); g(0) = g0 A fundamental and di-cult problem in difierential geometry is to flnd a standard metric satisfying some prescribed conditions over a Riemannian manifold. For in- stance, concerning the celebrated Yamabe problem (20), it is essential to flnd a metric with a constant scalar curvature; and for the constant Ricci curvature, one needs to solve an Einstein equation. The study of Ricci ∞ows, in general, is exactly to flnd a standard metric satisfying the given conditions, and to solve Ricci equation. The typical problem related to Ricci ∞ows is the following short-time existence theorem: Given a compact and smooth Riemannian manifold (M n ;g0), there exists a unique smooth solution g(t) deflned on a short-time-interval such that g(0) = g0. It is natural to ask that in which case the long-time existence theorem of Ricci ∞ows is tenable and the solution converges to a constant curvature metric. The" @default.
- W2184382450 created "2016-06-24" @default.
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- W2184382450 date "2010-01-01" @default.
- W2184382450 modified "2023-09-27" @default.
- W2184382450 title "On stability of Ricci ∞ows based on bounded curvatures" @default.
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