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arXiv · 2608.21053

A counterexample to the bounded mass property

Mingchen Xia·Kewei Zhang
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Abstract

A compact complex manifold has the bounded mass property if, for one (equivalently, every) Hermitian form $\omega$, the masses $\int_X(\omega+\mathrm{dd}^{\mathrm{c}}\varphi)^n$ are uniformly bounded over all smooth $\varphi$ with $\omega+\mathrm{dd}^{\mathrm{c}}\varphi>0$. 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.

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Mingchen Xia, Kewei Zhang. 2026-08-21. A counterexample to the bounded mass property. https://arxiv.org/abs/2608.21053

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