论文标题
Hermitian流形中的$ C^2 $域中的强大的Diederich-Fornæss索引
The Strong Diederich-Fornæss Index on $C^2$ Domains in Hermitian Manifolds
论文作者
论文摘要
对于一个相对紧凑的Stein域$ω$，带有$ c^2 $边界在Hermitian歧管$ m $中，我们考虑到强大的Diesterich-Fornæss索引，表示为$ df（ω）$：所有指数的至上$ 0 <η<1 $ $ 0 <η<1 $，以至于有些阳离子的多个$ - （$ - （$）的繁星点是$ - （ - （$）$ - （ - （ $（ - ρ）^η$ on $ω$，对于某些$ c^2 $定义函数$ρ$。我们将证明$ df（ω）$的特征是存在具有弯曲术语的Hermitian度量，当限制在Levi-form的空空间时，满足某些不平等的术语。
For a relatively compact Stein domain $Ω$ with $C^2$ boundary in a Hermitian manifold $M$, we consider the strong Diederich-Fornæss index, denoted $DF(Ω)$: the supremum of all exponents $0<η<1$ such that eigenvalues of the complex Hessian of $-(-ρ)^η$ are bounded below by some positive multiple of $(-ρ)^η$ on $Ω$ for some $C^2$ defining function $ρ$. We will show that $DF(Ω)$ is completely characterized by the existence of a Hermitian metric with curvature terms satisfying a certain inequality when restricted to the null-space of the Levi-form.
