Year: 2026
Type: preprint
Abstract: A compact complex manifold has the bounded mass property if, for one (equivalently, every) Hermitian form $ω$, the masses $\int_X(ω+\mathrm{dd}^{\mathrm{c}}φ)^n$ are uniformly bounded over all smooth $φ$ with $ω+\mathrm{dd}^{\mathrm{c}}φ>0$. We prove that this property fails on the Hopf threefold $(\mathbb C^3\setminus\{0\})/\langle z\mapsto\mathrm{e}^{-1}z\rangle$, answering a question of Boucksom--Guedj--Lu.
Source: arXiv (Cornell University)
Authors: Xia, Mingchen, Zhang, Kewei
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204090679
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