Lu Qi-Keng's problem for intersection of two complex ellipsoids

Tomasz Beberok

arXiv:1507.06181·math.CV·July 23, 2015

Lu Qi-Keng's problem for intersection of two complex ellipsoids

Tomasz Beberok

PDF

Open Access

TL;DR

This paper investigates the Lu Qi-Keng problem specifically for the intersection of two complex ellipsoids in three-dimensional complex space, providing insights into the properties of their Bergman kernels.

Contribution

It offers a novel analysis of the Lu Qi-Keng problem for a specific class of intersecting complex ellipsoids, extending previous studies to this geometric configuration.

Findings

01

Characterization of the Bergman kernel for the intersection

02

Conditions under which the intersection is a Lu Qi-Keng domain

03

New insights into complex ellipsoid intersections

Abstract

In this paper We investigate the Lu Qi-Keng problem for intersection of two complex ellipsoids ${z \in C^{3} : ∣ z_{1} ∣^{2} + ∣ z_{2} ∣^{q} < 1, ∣ z_{1} ∣^{2} + ∣ z_{3} ∣^{r} < 1}$ .

Peer Reviews

No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.

Videos

No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.

Taxonomy

TopicsMathematics and Applications · Advanced Differential Equations and Dynamical Systems · Meromorphic and Entire Functions