Characterization for Balls by Potential Function of Kähler-Einstein Metrics for Domains in C n
Characterization for Balls by Potential Function of Kähler-Einstein Metrics for Domains in C n
复制标题
DOI：
10.4310/cag.2005.v13.n2.a8
复制
发表时间：
2005
影响因子：
0.7
通讯作者：
S. Li
中科院分区：
文献类型：
--
作者：
S. Li
其中 ∂ρ 表示具有条目 ∂ρ ∂z1 、··· 、∂ρ ∂zn 的行向量。当 D 是 C 中的平滑有界严格伪凸域时，C. Fefferman 在 [7] 中给出了 (1.3) 的正式正解。 Cheng和Yau证明了正解的存在性[5]。此外，他们还证明了ρ ∈ Cn+3/2(D)。 Lee 和 Melrose [21] 给出了 ρ 的渐近展开式，这意味着 ρ ∈ Cn+2− (D)。当D是C中的光滑有界弱赝凸域时，Cheng和Yau[5]证明了存在完整的Kähler-Einstein度量。 Mok 和 Yau 后来在 [27] 中得到了关于存在完整的 Kähler-Einstein 度量的相同结果，而无需假设边界 ∂D 的平滑度。之前已经发现了几个关于 C 中单位球表征的非常有趣且基本的定理。例如，B.
where ∂ρ denotes the row vector with entries ∂ρ ∂z1 , · · · , ∂ρ ∂zn . When D is a smoothly bounded strictly pseudoconvex domain in C, a formal positive solution of (1.3) was given by C. Fefferman in [7]. The existence of a positive solution was proved by Cheng and Yau [5]. Moreover, they also proved that ρ ∈ Cn+3/2(D). Lee and Melrose [21] gave an asymptotic expansion for ρ, which implies that ρ ∈ Cn+2− (D). When D is a smoothly bounded weakly pseudoconvex domain in C, it was proved by Cheng and Yau [5] that there is a complete Kähler–Einstein metric. The same result on the existence of a complete Kähler-Einstein metric was obtained later by Mok and Yau in [27] without an assumption on the smoothness of the boundary ∂D. Several very interesting and fundamental theorems on the characterization of the unit ball in C have bee discovered before. For example, B.