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Volumes of components of Lelong upper level sets II (2404.14058v1)
Published 22 Apr 2024 in math.CV and math.AG
Abstract: Let $X$ be a compact K\"ahler manifold of dimension $n$, and let $T$ be a closed positive $(1,1)$-current in a nef cohomology class on $X$. We establish an optimal upper bound for the volume of components of Lelong upper level sets of $T$ in terms of cohomology classes of non-pluripolar self-products of $T$.
- J.-P. Demailly, Complex analytic and differential geometry. http://www.fourier.ujf-grenoble.fr/~demailly.
- D.-V. Vu, Densities of currents on non-Kähler manifolds. https://doi.org/10.1093/imrn/rnz270. Int. Math. Res. Not. IMRN.
- Â , Loss of mass of non-pluripolar products. arXiv:2101.05483, 2021.
- Â , Derivative of volumes of big cohomology classes. arXiv:2307.15909, 2023.
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