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We will give a simple proof that the metric of any compact Yamabe gradient soliton (M,g) is a metric of constant scalar curvature when the dimension of the manifold n>2.
B. Chow, The Yamabe flow on locally conformally flat manifolds with positive Ricci curvature
1992
Earlier work this paper cites.
M. Del Pino, M. Sáez, On the extinction profile for solutions of u t = Δ u N − 2 N + 2 u_{t}=\Delta u^{\frac{N-2}{N+2}}
2001
Earlier work this paper cites.
S. Brendle, Convergence of the Yamabe flow for arbitrary initial energy
2005
Cited alongside, same era.
S. Brendle, Convergence of the Yamabe flow in dimension 6 and higher
2007
Cited alongside, same era.
P. Daskalopoulos and N. Sesum, The classification of locally conformally flat Yamabe solitons
Cited in the paper.
L. Ma and L. Cheng, Properties of complete non-compact Yamabe solitons
Cited in the paper.
S.Y. Hsu, Singular limit and exact decay rate of a nonlinear elliptic equation
Cited in the paper.
A. Burchard, R.J. Mccan and A. Smith, Explicit Yamabe flow of an asymmetric cigar
2008
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