Eigenvalues of the Laplace operator with potential under the backward Ricci flow on locally homogeneous 3-manifolds

no code implementations • 29 Jan 2021 • Songbo Hou, Shusen Yang

Let $\lambda(t)$ be the first eigenvalue of $-\Delta+aR\, (a>0)$ under the backward Ricci flow on locally homogeneous 3-manifolds, where $R$ is the scalar curvature.

Differential Geometry 53E20, 58C40

Gradient estimates for the nonlinear parabolic equation with two exponents on Riemannian manifolds

no code implementations • 13 Jan 2021 • Songbo Hou

The special types of such equation include the Fisher-KPP equation, the parabolic Allen-Cahn equation and the Newell-Whitehead equation.

Differential Geometry 58J35, 35K55