Mingchen Xia

A counterexample to the bounded mass property

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...