L^1 metric geometry of big cohomology classes

@article{Darvas2018L1MG,
title={L^1 metric geometry of big cohomology classes},
author={Tam'as Darvas and Eleonora Di Nezza and Chinh H. Lu},
journal={arXiv: Differential Geometry},
year={2018}
}
• Published 31 January 2018
• Mathematics
• arXiv: Differential Geometry
Suppose $(X,\omega)$ is a compact K\"ahler manifold of dimension $n$, and $\theta$ is closed $(1,1)$-form representing a big cohomology class. We introduce a metric $d_1$ on the finite energy space $\mathcal{E}^1(X,\theta)$, making it a complete geodesic metric space. This construction is potentially more rigid compared to its analog from the K\"ahler case, as it only relies on pluripotential theory, with no reference to infinite dimensional $L^1$ Finsler geometry. Lastly, by adapting the… Expand
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