论文标题
可移动套件和$ l^p $ - 歧管和度量度量空间上的唯一性
Removable sets and $L^p$-uniqueness on manifolds and metric measure spaces
论文作者
论文摘要
我们在度量测量空间上研究对称扩散操作员。我们的主要问题是，如果从空间中删除了一个小的封闭套件，则操作员对合适核心的限制是否基本上是自我伴侣或$ l^p $ - 唯一的。效果取决于删除集的大小，我们在能力和Hausdorff尺寸方面提供了临界大小的特征。作为一个关键工具，我们证明了非负函数电位的截断结果。我们将结果应用于Riemannian和riemannian歧管以及满足曲率维度条件的度量空间的拉普拉斯操作员。对于具有双面RICCI曲率界限的非碰撞RICCI极限空间，我们观察到自偶会Laplacian已经由常规部分的经典laplacian完全确定。
We study symmetric diffusion operators on metric measure spaces. Our main question is whether or not the restriction of the operator to a suitable core continues to be essentially self-adjoint or $L^p$-unique if a small closed set is removed from the space. The effect depends on how large the removed set is, and we provide characterizations of the critical size in terms of capacities and Hausdorff dimension. As a key tool we prove a truncation result for potentials of nonnegative functions. We apply our results to Laplace operators on Riemannian and sub-Riemannian manifolds and on metric measure spaces satisfying curvature dimension conditions. For non-collapsing Ricci limit spaces with two-sided Ricci curvature bounds we observe that the self-adjoint Laplacian is already fully determined by the classical Laplacian on the regular part.
