Precise Gaussian estimates of heat kernels on asymptotically flat Riemannian manifolds with poles
Precise Gaussian estimates of heat kernels on asymptotically flat Riemannian manifolds with poles
复制标题
具有极点的渐进平坦黎曼流形上热核的精确高斯估计
DOI：
10.1142/9789812702241_0001
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发表时间：
2004
影响因子：
1.7
通讯作者：
S. Aida
中科院分区：
文献类型：
--
作者：
S. Aida
我们给出精确的高斯上限和下限估计的热核黎曼流形的极点的假设下，黎曼曲率张量到0足够快的无穷远。在额外的曲率假设下，我们给出了热核的对数导数的估计。证明依赖于Elworthy-Truman的热核公式和Elworthy和Yor对某些随机流的导数过程的观察。作为它们的应用，我们证明了这类黎曼流形上钉扎路空间上的对数Sobolev不等式。
We give precise Gaussian upper and lower bound estimates on heat kernels on Riemannian manifolds with poles under assumptions that the Riemannian curvature tensor goes to 0 sufficiently fast at infinity. Under additional assumptions on the curvature, we give estimates on the logarithmic derivatives of the heat kernels. The proof relies on the Elworthy-Truman’s formula of heat kernels and Elworthy and Yor’s observation on the derivative process of certain stochastic flows. As an application of them, we prove logarithmic Sobolev inequalities on pinned path spaces over such Riemannian manifolds.