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Mathematics > Complex Variables

Title: Isometries in the diamond

Authors: Anand Chavan, Włodzimierz Zwonek
(Submitted on 16 Mar 2024)
Abstract: We show the (anti)holomorphicity of smooth Kobayashi isometries of the diamond, the domain defined as $\triangle:=\{z\in\mathbb C^2:|z_1|+|z_2|<1\}$. Additionally, we discuss the problem of uniqueness of real geodesics, left inverses and strict convexity of indicatrices.
Comments: 15 pages
Subjects: Complex Variables (math.CV)
MSC classes: 32F45
Cite as: arXiv:2403.11031 [math.CV]
  (or arXiv:2403.11031v1 [math.CV] for this version)

Submission history

From: Wlodzimierz Zwonek [view email]
[v1] Sat, 16 Mar 2024 22:34:30 GMT (51kb)
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