Boundary behavior of the Kobayashi metric near a point of infinite type

Abstract

Under a potential-theoretical hypothesis named $f$-Property with $f$ satisfying ${\int }_t^{\infty }\frac{da}{af(a)}<\infty$, we show that the Kobayashi metric $K(z,X)$ on a weakly pseudoconvex domain $\Om$, satisfies the estimate $K(z,X)\ge Cg(δ_\Om(x)^{-1})|X|$ for any $X\in T^{1,0}\Om$ where $(g(t){)}^{-1}$ denotes the above integral and $δ_\Om(z)$ is the distance from $z$ to $b\Om$.

15 pages

References in corpus (2)

• A general method of weights in the d-bar-Neumann problem
• Supnorm and f-Holder estimates for di-bar on convex domains of general type in C^2

Cited by in corpus (1)

• Hölder regularity of the solution to the complex Monge-Ampère equation with $L^p$ density