Bi-Hölder extensions of quasi-isometries on complex domains. (English) Zbl 1487.32062
Summary: In this paper, we prove some results on bi-Hölder extensions not only for biholomorphisms but also for more general Kobayashi metric quasi-isometries between the domains. Furthermore, we establish the Gehring-Hayman type theorems on certain complex domains which play an important role through the paper. Then by applying the above results, we show the bi-Hölder equivalence between the Euclidean boundary and the Gromov boundary of bounded convex domains which are Gromov hyperbolic with respect to their Kobayashi metrics.
MSC:
| 32F45 | Invariant metrics and pseudodistances in several complex variables |
| 32F18 | Finite-type conditions for the boundary of a domain |
| 32T15 | Strongly pseudoconvex domains |
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