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arXiv · 2107.09522

Some Properties of Balanced Hyperbolic Compact Complex Manifolds

Samir Marouani·Dan Popovici
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Abstract

We prove several vanishing theorems for the cohomology of balanced hyperbolic manifolds that we introduced in our previous work and for the $L^2$ harmonic spaces on the universal cover of these manifolds. Other results include a Hard Lefschetz-type theorem for certain compact complex balanced manifolds and the non-existence of certain $L^1$ currents on the universal covering space of a balanced hyperbolic manifold.

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Samir Marouani, Dan Popovici. 2021-07-20. Some Properties of Balanced Hyperbolic Compact Complex Manifolds. https://doi.org/10.1142/s0129167x22500197

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