Abstract
By revisiting Tian’s peak section method, we obtain a localization principle of the Bergman kernels on Kähler manifolds with complex hyperbolic cusps, which is a generalization of Auvray–Ma–Marinescu’s (Math Ann 379:51–1002, 2021) localization result Bergman kernels on punctured Riemann surfaces . Then we give some further estimates when the metric on the complex hyperbolic cusp is a Kähler–Einstein metric or when the manifold is a quotient of the complex ball. By applying our method directly to Poincaré type cusps, we also get a partial localization result.
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Acknowledgements
I would like to express my deepest gratitude to Professor Gang Tian, my supervisor, for his constant encouragement and guidance. The author is supported by National Key R &D Program of China 2020YFA0712800.
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Zhou, S. Peak sections and Bergman kernels on Kähler manifolds with complex hyperbolic cusps. Math. Ann. (2024). https://doi.org/10.1007/s00208-024-02798-9
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DOI: https://doi.org/10.1007/s00208-024-02798-9