论文标题
Schrödinger热核的尖锐高斯上限梯度收缩Ricci soliton
Sharp Gaussian upper bounds for Schrödinger heat kernel on gradient shrinking Ricci solitons
论文作者
论文摘要
关于梯度缩小的Ricci孤子，我们观察到，对Schrödinger热核的研究似乎比经典的热核更自然。在本文中，我们在完全梯度缩小的Ricci孤子子上得出了Schrödinger热核的尖锐高斯上限。作为应用，我们证明了Schrödinger操作员绿色功能的急剧上限。我们还证明了Schrödinger操作员特征值的急剧下限。这些尖锐的病例都是在欧几里得高斯萎缩的ricci孤子中实现的。
On gradient shrinking Ricci solitons, we observe that the study of Schrödinger heat kernel seems to be more natural than the classical heat kernel. In this paper we derive sharp Gaussian upper bounds for the Schrödinger heat kernel on complete gradient shrinking Ricci solitons. As applications, we prove sharp upper bounds for the Green's function of the Schrödinger operator. We also prove sharp lower bounds for eigenvalues of the Schrödinger operator. These sharp cases are all achieved at Euclidean Gaussian shrinking Ricci solitons.
