Yau's finite-volume quotient conjecture for bounded pseudoconvex domains

About 8 years old · traced to

Let DearrowCnD earrow\mathbb{C}^n (n≥2)(n\geq 2) be a bounded pseudoconvex domain whose boundary is C2C^2-smooth. Assume that DD has an open quotient of finite volume in the sense of Kähler–Einstein measure. Yau's conjecture. The domain DD is biholomorphic to the unit ball in Cn\mathbb{C}^n. This conjecture asks whether the compact-quotient hypothesis in the Wong–Rosay theorem can be replaced by finite volume. The source reports partial results and notes a later claim by A. Zimmer of a solution; the supplied status is unknown, so the database status remains open.

References

Primary source

Kefeng Liu and Yunhui Wu, “Geometry of complex bounded domains with finite-volume quotients”, arXiv:1801.00459 (2018).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.