论文标题
定量Sobolev扩展和Neumann Heat内核，用于整体RICCI曲率条件
Quantitative Sobolev extensions and the Neumann heat kernel for integral Ricci curvature conditions
论文作者
论文摘要
我们证明了在riemannian歧管中某些统一类别域的Sobolev扩展运算符的存在，并且仅取决于其边界附近的几何形状，其明确统一绑定在规范上。我们使用此定量估计值获得均匀的Neumann热核上限，并为Neumann热方程的正溶液进行梯度估计，假设边界上的RICCI曲率条件和几何条件，则可以获得Neumann热方程的正溶液。这些估计还意味着在考虑域的第一个neumann特征值上的定量下限。
We prove the existence of Sobolev extension operators for certain uniform classes of domains in a Riemannian manifold with an explicit uniform bound on the norm depending only on the geometry near their boundaries. We use this quantitative estimate to obtain uniform Neumann heat kernel upper bounds and gradient estimates for positive solutions of the Neumann heat equation assuming integral Ricci curvature conditions and geometric conditions on the boundary. Those estimates also imply quantitative lower bounds on the first Neumann eigenvalue of the considered domains.
