高维曲面的Pizzetti公式和Cauchy公式：分布方法
Pizzetti and Cauchy formulae for higher dimensional surfaces: a distributional approach
摘要：
本文从分布的角度研究了Stiefel流形的Pizzetti型公式和切向Dirac算子的Cauchy型公式。首先，我们说明了一个一般的分配方法的$\mathbb R^m$的积分流形定义的$k$方程$φ_1(\underline{x})=\ldots=φ_k(\underline{x})=0$。接下来，我们应用这种方法来获得一个替代的证明Pizzetti公式的实Stiefel流形$SO(m)/SO(m-k)$。此外，对面向不变式的积分给出了分布解释。特别地，我们得到了嵌入$(m-k)$维光滑曲面上切向Dirac算子的分布Cauchy定理.
英文摘要：
In this paper, we study Pizzetti-type formulas for Stiefel manifolds and Cauchy-type formulas for the tangential Dirac operator from a distributional perspective. First we illustrate a general distributional method for integration over manifolds in $\mathbb R^m$ defined by means of $k$ equations $φ_1(\underline{x})=\ldots=φ_k(\underline{x})=0$. Next, we apply this method to derive an alternative proof of the Pizzetti formulae for the real Stiefel manifolds $SO(m)/SO(m-k)$. Besides, a distributional interpretation to invariant oriented integration is provided. In particular, we obtain a distributional Cauchy theorem for the tangential Dirac operator on an embedded $(m-k)$-dimensional smooth surface.
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