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Boundary rigidity of Gromov hyperbolic spaces

open access: yesGeometriae Dedicata
We introduce the concept of boundary rigidity for Gromov hyperbolic spaces. We show that a proper geodesic Gromov hyperbolic space with a pole is boundary rigid if and only if its Gromov boundary is uniformly perfect. As an application, we show that for a non-compact Gromov hyperbolic complete Riemannian manifold or a Gromov hyperbolic uniform graph ...
Liang, Hao, Zhou, Qingshan
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Sharp estimates of the Kobayashi metric and Gromov hyperbolicity

open access: yesJournal of Mathematical Analysis and Applications, 2008
Let D be a smooth relatively compact and strictly J-pseudoconvex domain in a four dimensional almost complex manifold (M,J). We give sharp estimates of the Kobayashi metric. Our approach is based on an asymptotic quantitative description of both the domain D and the almost complex structure J near a boundary point.
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