27 citations · 78 across the 9 of their papers we have counts for
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Ricci Flow method in the existence problem of the K"ahler-Einstein metrics
Liu Chao
This note illustrates the Ricci flow method based on the Cao.H.D's paper[1] and Yau.S.T's paper[4], and tries to explain the method in detail, especially in some calculations. Jian…
Fully nonlinear gravitational instabilities for expanding Newtonian universes with inhomogeneous pressure and entropy: Beyond the Tolman's solution
Chao Liu
Nonlinear gravitational instability is a crucial way to comprehend the clustering of matter and the formation of nonlinear structures in both the Universe and stellar systems. Howe…
Blowups for a class of second order nonlinear hyperbolic equations: A reduced model of nonlinear Jeans instability
Chao Liu
Understanding the formation of nonlinear structures in the universe and stellar systems is crucial. The nonlinear Jeans instability plays a key role in these formation processes. I…
Rigorous proof of slightly nonlinear Jeans instability in the expanding Newtonian universe
Chao Liu, Yiqing Shi
Due to the nonlinearity of the Euler{Poisson equations, it is possible that the nonlinear Jeans instability may lead to a faster density growing rate than the rate in the standard…
Future global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions
Chao Liu, Todd A. Oliynyk, Jinhua Wang
We establish the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in spacetime dimen…