5 citations · 9 across the 13 of their papers we have counts for
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Eigenvalues of the Laplace operator with potential under the backward Ricci flow on locally homogeneous 3-manifolds
Songbo Hou, Shusen Yang
Let be the first eigenvalue of under the backward Ricci flow on locally homogeneous 3-manifolds, where is the scalar curvature. In the Bianchi case, we g…
Gradient estimates for the nonlinear parabolic equation with two exponents on Riemannian manifolds
Songbo Hou
In this paper, we study the nonlinear parabolic equation with two exponents on complete noncompact Riemannian maniflods. The special types of such equation include the Fisher-KPP e…
Gradient estimates for the Allen-Cahn equation on Riemannian manifolds
Songbo Hou
In this paper, we consider bounded positive solutions to the Allen-Cahn equation on complete noncompact Riemannian manifolds without boundary. We derive gradient estimates for thos…
Eigenvalues under the backward Ricci flow on locally homogeneous closed 3-manifolds
Songbo Hou
In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized backward Ricci flow, construct various quantities which are…
Eigenvalues under the Ricci flow of model geometries
Songbo Hou
In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized Ricci flow of model geometries. In every Bianchi class, we…
Quasi-convergence of the Ricci flow on locally homogeneous closed 4-manifolds
Songbo Hou
We study the quasi-convergence equivalence of some families of metrics on locally homogeneous closed 4-manifolds with trivial isotropy group, and identify the dimension of each equ…