具有横截对称的次黎曼流形的随机分析
Stochastic analysis on sub-Riemannian manifolds with transverse symmetries
摘要：
证明了具有横对称的子黎曼流形上热半群导数的一个几何意义的随机表示。这个表示是从研究1-形式上的子拉普拉斯算子的Bochner-Weitzenbock型公式中得到的。作为结果，我们在自然的整体几何条件下证明了新的亚椭圆热半群梯度界。结果是新的，即使在海森堡群的情况下，这是一个最简单的例子，一个子黎曼流形的横向对称。
英文摘要：
We prove a geometrically meaningful stochastic representation of the derivative of the heat semigroup on sub-Riemannian manifolds with tranverse symmetries. This representation is obtained from the study of Bochner-Weitzenbock type formulas for sub-Laplacians on 1-forms. As a consequence, we prove new hypoelliptic heat semigroup gradient bounds under natural global geometric conditions. The results are new even in the case of the Heisenberg group which is the simplest example of a sub-Riemannian manifold with transverse symmetries.
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