论文标题
驯服空间 - 带有分布值的RICCI边界的Dirichlet空间
Tamed spaces -- Dirichlet spaces with distribution-valued Ricci bounds
论文作者
论文摘要
我们开发了驯服空间的理论，这些空间是Dirichlet空间，在Ricci曲率上具有分布值的下限，并从Eulerian的角度研究了这些空间。为此，我们通过广泛的分布详细分析了Dirichlet形式的奇异扰动。然后，使用扰动的能量形式以Bochner不平等的集成版本来制定分布的RICCI结合，并概括众所周知的Bakry-émery-émery曲率差异条件。除其他外，我们还显示了分布ricci的等效性与热半群的梯度估计值，从驯服分布引起的Feynman-KAC半群以及功能不平等方面的后果。我们给出了许多驯服空间的例子，包括尤其是具有内部奇异性或奇异边界行为的Riemannian歧管。
We develop the theory of tamed spaces which are Dirichlet spaces with distribution-valued lower bounds on the Ricci curvature and investigate these from an Eulerian point of view. To this end we analyze in detail singular perturbations of Dirichlet form by a broad class of distributions. The distributional Ricci bound is then formulated in terms of an integrated version of the Bochner inequality using the perturbed energy form and generalizing the well-known Bakry-Émery curvature-dimension condition. Among other things we show the equivalence of distributional Ricci bounds to gradient estimates for the heat semigroup in terms of the Feynman-Kac semigroup induced by the taming distribution as well as consequences in terms of functional inequalities. We give many examples of tamed spaces including in particular Riemannian manifolds with either interior singularities or singular boundary behavior.
