论文标题
Yau和Souplet-Zhang类型梯度估计在Riemannian歧管上，边界在dirichlet边界条件下
Yau and Souplet-Zhang type gradient estimates on Riemannian manifolds with boundary under Dirichlet boundary condition
论文作者
论文摘要
在本文中，在带有边界的Riemannian歧管上，我们建立了YAU类型梯度估计值，并在Dirichlet边界条件下建立了谐波函数的Liouville定理。在类似的环境下，我们还制定了souplet-zhang型梯度估计值，而liouville定理则用于对热方程式的古代解决方案。
In this paper, on Riemannian manifolds with boundary, we establish a Yau type gradient estimate and Liouville theorem for harmonic functions under Dirichlet boundary condition. Under a similar setting, we also formulate a Souplet-Zhang type gradient estimate and Liouville theorem for ancient solutions to the heat equation.
