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- W3022427303 abstract "In this paper we establish Gehring-Hayman type theorems for some complex domains. Suppose that $Omegasubset mathbb{C}^n$ is a bounded $m$-convex domain with Dini-smooth boundary, or a bounded strongly pseudoconvex domain with $C^2$-smooth boundary. Then we prove that the Euclidean length of Kobayashi geodesic $[x,y]$ in $Omega$ is less than $c_1|x-y|^{c_2}$. Furthermore, if $Omega$ endowed with the Kobayashi metric is Gromov hyperbolic, then we can generalize this result to quasi-geodesics with respect to Bergman metric, Caratheodory metric or Kahler-Einstein metric. As applications, we prove the bi-Holder equivalence between the Euclidean boundary and the Gromov boundary. Moreover, by using this boundary correspondence, we can show some extension results for biholomorphisms, and more general rough quasi-isometries with respect to the Kobayashi metrics between the domains." @default.
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- W3022427303 date "2020-05-06" @default.
- W3022427303 modified "2023-09-27" @default.
- W3022427303 title "The Gehring-Hayman type theorems on complex domains." @default.
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