Peter Hästö (University of Helsinki/Norwegian University of Science and Technology)
Arc-wise hyperbolic metrics
Abstract.
Let G be a domain in R^n. A metric is said to be arc-wise hyperbolic if the following condition holds: if B is a ball in G which touches the boundary at two points, and C is the arc of a circle perpendicular to B at these points that joins them in B, then the metric restricted to C equals the hyperbolic metric. Examples of metrics with this property are the Apollonian metric, Ferrand's metric, the Kulkarni-Pinkal metric and Seittenranta's metric. In this talk I will discuss the problem of determining the isometries of such metrics, with a focus on the Apollonian metric.

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