Proposition 17.10.52042C299A40E

Proposition 17.10.5.2042C299A40E Let $g$ be a smooth real function on $X$. Let $\theta '=\theta +\mathrm{dd}^{\mathrm{c}}g$. Suppose that $(\varphi _ t)_{t\in [0,1]}$ is a subgeodesic in $\mathrm{PSH}(X,\theta )$. Then $(\varphi _ t-g)_{t\in [0,1]}$ is a subgeodesic in $\mathrm{PSH}(X,\theta ')$.