实解析黎曼流形的Grauert管上的多位势论，I
Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I
摘要：
我们开发的Grauert管的实际解析黎曼流形（M，g）的一些基本概念的多位势论，如Siciak极值函数的类似物。其基本思想是使用本征函数的解析延拓来代替多能理论中正线丛的多项式或幂部分。解析连续的泊松波核起着Bergman核的作用。主要结果是外尔定律在复杂的区域，分布复杂的零点的本征函数的局部对称空间，估计三重产品的本征函数。
英文摘要：
We develop analogues for Grauert tubes of real analytic Riemannian manifolds (M,g) of some basic notions of pluri-potential theory, such as the Siciak extremal function. The basic idea is to use analytic continuations of eigenfunctions in place of polynomials or sections of powers of positive line bundles for pluripotential theory. The analytically continued Poisson-wave kernel plays the role of Bergman kernel. The main results are Weyl laws in the complex domain, distribution of complex zeros of eigenfunctions on locally symmetric spaces, and estimates of triple products of eigenfunctions.
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