论文标题
加热核与应用的共形扰动
Conformal Perturbation of Heat Kernels with applications
论文作者
论文摘要
令$（m，g）$为$ n \ ge 2 $的平滑n维riemannian歧管。考虑共形扰动$ \ tilde {g} = h g $其中$ h $是$ m $上的平滑有限的正函数。用$ \ tilde {p} _t（x，y）$ vicrolds $（m，\ tilde {g}）$的加热核。在本文中，我们得出了$ \ tilde {p} _t（x，y）$的上限和梯度估计。
Let $(M, g)$ be a smooth n-dimensional Riemannian manifold for $n\ge 2$. Consider the conformal perturbation $\tilde{g}=h g$ where $h$ is a smooth bounded positive function on $M$. Denote by $\tilde{p}_t(x,y)$ the heat kernel of manifolds $(M, \tilde{g})$. In this paper, we derive the upper bounds and gradient estimates of $\tilde{p}_t(x,y)$.
