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arXiv · 1504.07914

Bergman theory of certain generalized Hartogs triangles

Luke Edholm
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Abstract

The Bergman theory of domains $\{ |{z_{1} |^{\gamma}} < |{z_{2}} | < 1 \}$ in $\mathbb{C}^2$ is studied for certain values of $\gamma$, including all positive integers. For such $\gamma$, we obtain a closed form expression for the Bergman kernel, $\mathbb{B}_{\gamma}$. With these formulas, we make new observations relating to the Lu Qi-Keng problem and analyze the boundary behavior of $\mathbb{B}_{\gamma}(z,z)$.

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Luke Edholm. 2015-04-29. Bergman theory of certain generalized Hartogs triangles. https://doi.org/10.2140/pjm.2016.284.327

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