AI 中文总结
该研究针对紧复流形的有界质量性质，通过证明Hopf三重曲面不具备该性质，解答了Boucksom–Guedj–Lu提出的相关问题。
AI 中文摘要
紧复流形具有有界质量性质，当对任意（等价于任一）埃尔米特形式ω，所有满足ω+dd^cφ>0的光滑函数φ对应的质量∫_X(ω+dd^cφ)^n均一致有界。我们证明该性质在Hopf三重曲面（(C^3\{0})/⟨z↦e⁻¹z⟩）上不成立，解答了Boucksom–Guedj–Lu提出的问题。
英文摘要
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.
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