论文标题
高斯的上限，用于不断发展的歧管上的热核
Gaussian upper bounds for the heat kernel on evolving manifolds
论文作者
论文摘要
在本文中，我们证明了通过固有几何流量演变的封闭歧管上的加权热算子的热核的一般且相当灵活的上限。该证明是基于对数Sobolev的不等式和沿流量的加权操作员的超包估计值的，而在非进化歧管的情况下，戴维斯先前使用的方法。该结果直接暗示着在不断发展的距离函数上的某些边界下热核的高斯型上限。特别是，我们发现了由RICCI流动以有界曲率或正ricci曲率进化的歧管上的高斯热核边界的新证明。我们还为一类其他几何流量获得了类似的热核边界。
In this article, we prove a general and rather flexible upper bound for the heat kernel of a weighted heat operator on a closed manifold evolving by an intrinsic geometric flow. The proof is based on logarithmic Sobolev inequalities and ultracontractivity estimates for the weighted operator along the flow, a method which was previously used by Davies in the case of a non-evolving manifold. This result directly implies Gaussian-type upper bounds for the heat kernel under certain bounds on the evolving distance function; in particular we find new proofs of Gaussian heat kernel bounds on manifolds evolving by Ricci flow with bounded curvature or positive Ricci curvature. We also obtain similar heat kernel bounds for a class of other geometric flows.
