We show that any generalized smooth distribution on a smooth manifold, possibly of non-constant rank, admits a Riemannian metric. Using such a metric, we attach a Laplace operator to any smooth distribution as such. When the underlying manifold is compact, we show that it is essentially self-adjoint. Viewing this Laplacian in the longitudinal pseudodifferential calculus of the smallest singular foliation which includes the distribution, we prove hypoellipticity.

中文翻译：

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用于广义平滑分布的黎曼度量和拉普拉斯算子

我们表明，在可能具有非常数秩的平滑流形上的任何广义平滑分布都承认黎曼度量。使用这样的度量，我们将拉普拉斯算子附加到任何平滑分布上。当底层流形是紧致的时，我们证明它本质上是自伴的。在包含分布的最小奇异叶理的纵向伪微分演算中查看这个拉普拉斯算子，我们证明了亚椭圆性。