L^1 metric geometry of big cohomology classes

  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},
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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