Some remarks on the geodesics and the boundary asymptotics of the Kobayashi--Fuks metric

Dr. Debaprasanna Kar, IISER Pune

Speaker	Dr. Debaprasanna Kar, IISER Pune
When	Feb 13, 2023 from 02:00 PM to 03:00 PM
Where	via zoom
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Abstract: This talk will be divided into two parts. In the first part, we will derive a few results on the geodesics of the Kobayashi--Fuks metric on strongly pseudoconvex domains. In particular, we will show the existence of closed geodesics with prescribed homotopy class when the domain is non-simply connected and strongly pseudoconvex. We will also prove the existence of geodesic spirals for the Kobayashi--Fuks metric on smoothly bounded planar domains. The second part of the talk will be devoted to studying the boundary asymptotics of the Kobayashi--Fuks metric on the class of h-extendible domains. Here, we derive the non-tangential boundary limits of the Kobayashi--Fuks metric and its Riemannian volume element by establishing some stability results on h-extendible model domains.

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