Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I

机译：plauert管的Pluri-Persity理论真正的分析riemannian歧管，I

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Analogues of the some basic notions of pluri-potential theory on strictly pseudo-convex domains in C~m are developed for Grauert tubes M_T in complexifications of real analytic Riemannian manifolds (M, g). In particular, the normalized logarithm of the complexified spectral projector ∏_(Iλ)~C (ζ,ζ-bar) is the analogue of the Siciak-Zaharjuta extremal pluri-subharmonic function. It is shown that 1/λ log ∏_(I/λ) (ζ,ζ-bar)→√p(ζ), where √p is the Grauert tube function. We give several applications to analytic continuations of eigenfunctions: to norm estimates, triple product integrals and to complex nodal sets.

机译：C〜M中严格伪凸域的Pluri-Persity理论的一些基本概念的类似物是用于真正分析riemannian歧管（M，G）的Grauert Tubes M_T的Grauert管M_T。特别地，复杂的光谱投影仪π_（iλ）~c（ζ，ζ栏）的归一化对数是SiCiAk-Zaharjuta极值Pluri-Sumharmonic功能的类似物。结果表明，1 /λlogπ_（i /λ）（ζ，ζ栏）→√p（ζ），其中√p是grauert管功能。我们将若干应用程序分析了实体功能的分析：常规估计，三重产品积分以及复杂的节点集。

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《International Conference on Spectral Geometry》|2012年||共41页
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作者
Steve Zelditch;
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中图分类 O657.3-532;
关键词
Pluri-potential; theory; Riemannian manifolds;

机译：pluri-poluate;理论;riemannian歧管;

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1. On rigidity of Grauert tubes over homogeneous Riemannian manifolds [J] . Kan SJ Journal fur die Reine und Angewandte Mathematik . 2004,第0期

机译：关于齐次黎曼流形上的Grauert管的刚度
2. On rigidity of Grauert tubes over Riemannian manifolds of constant curvature [J] . Su-Jen Kan, Daowei Ma Mathematische Zeitschrift . 2002,第2期

机译：常曲率黎曼流形上的Grauert管的刚度
3. Grauert's theorem for subanalytic open sets in real analytic manifolds [J] . Daniel B., Fernandes T.M. Studia mathematica . 2011,第3期

机译：实解析流形中次解析开放集的Grauert定理
4. Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I [C] . Steve Zelditch International Conference on Spectral Geometry . 2012

机译：plauert管的Pluri-Persity理论真正的分析riemannian歧管，I
5. Superiority of Bayes Estimators over the Mle in High Dimensional Models on Compact Riemannian Manifolds and Its Implication for Nonparametric Bayes Theory [D] . Oliver, Rachel. 2020

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7. Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I [O] . 2012

机译：plauert管的Pluri-Persity理论真正的分析riemannian歧管，I

Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I

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