4 papers
A counterexample to the bounded mass property
Mingchen Xia, Kewei Zhang
A compact complex manifold has the bounded mass property if, for one (equivalently, every) Hermitian form , the masses are uniformly boun…
The trace operator of quasi-plurisubharmonic functions on compact Kähler manifolds
Tamás Darvas, Mingchen Xia
We introduce the trace operator for quasi-plurisubharmonic functions on compact Kähler manifolds, allowing to study the singularities of such functions along submanifolds where the…
Operations on transcendental non-Archimedean metrics
Mingchen Xia
We define the basic pluripotential-theoretic operations in terms of the transcendental theory of non-Archimedean metrics introduced in \cite{DXZ23}. In particular, we establish tha…
Transcendental Okounkov bodies
Tamás Darvas, Rémi Reboulet, David Witt Nyström +2
We show that the volume of transcendental big -classes on compact Kähler manifolds can be realized by convex bodies, thus answering questions of Lazarsfeld-Mustaţă and Deng.…