Higher order Bergman functions and explicit construction of moduli space for complete Reinhardt domains

Du, Rong; Yau, Shing‐Tung

doi:10.4310/jdg/1251122546

Cited by 2 publications

(3 citation statements)

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“…This result is much stronger than the corresponding result obtained by Sunada [17]. In principle, the method introduced by Du and Yau [4] could be used to study the biholomorphic equivalence problem or moduli problem for more general pseudoconvex domains in A n -variety.…”

Section: Introductionmentioning

confidence: 78%

“…In this section, we shall recall some basic definitions and results in our previous papers [4,20] which will facilitate our subsequent discussion. Let M be a pseudoconvex complex manifold and A be a compact complex analytic variety in the interior of M .…”

Section: Preliminariesmentioning

confidence: 99%

“…The results of this paper will solve these problems. Recently Du and Yau [4] studied the moduli problem of complete Reinhardt domains in C 2 from a different point of view. The main tool to solve this moduli problem with geometry information is the new biholomorphic invariant Bergman function defined by Yau [20] on pseudoconvex domains in a variety with only isolated singularity.…”

Section: Introductionmentioning

confidence: 99%

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Explicit construction of moduli space of bounded complete Reinhardt domains in $\mathbb{C}^n$

Gao

Yau³

2010

Communications in Analysis and Geometry

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One of the most fundamental problems in complex geometry is to determine when two bounded domains in C n are biholomorphically equivalent. Even for complete Reinhardt domains, this fundamental problem remains unsolved completely for many years. Using the Bergmann function theory, we construct an infinite family of numerical invariants from the Bergman functions for complete Reinhardt domains in C n . These infinite family of numerical invariants are actually a complete set of invariants if the domains are pseudoconvex with C 1 boundaries. For bounded complete Reinhardt domains with real analytic boundaries, the complete set of numerical invariants can be reduced dramatically although the set is still infinite. As a consequence, we have constructed the natural moduli spaces for these domains for the first time.

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Section: Introductionmentioning

confidence: 78%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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