Abstract
We prove a degenerate Donnelly–Fefferman theorem. Applications to local non-integrability of plurisubharmonic functions and \(L^2\) boundary decay estimates of the Bergman kernel are given.
Dedicated to Professor Kang-Tae Kim on the occasion of his 60-th birthday.
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Berndtsson, B.: Weighted estimates for the \({\bar{\partial }}\)-equation. In: McNeal, J.D. (ed.) Complex Analysis and Complex Geometry, pp. 43–57. de Gruyter (2001)
Berndtsson, B.: The openness conjecture for plurisubharmonic functions. arXiv:1305.5781
Berndtsson, B., Charpentier, P.: A Sobolev mapping property of the Bergman kernel. Math. Z. 235, 1–10 (2000)
Blocki, Z.: Cauchy-Riemann meet Monge-Amp\(\grave{e}\)re. Bull. Math. Sci. 4, 433–480 (2014)
Chen, B.-Y.: A simple proof of the Ohsawa-Takegoshi extension theorem. arXiv:1105.2430v1
Chen, B.-Y.: Parameter dependence of the Bergman kernels. Adv. Math. 299, 108–138 (2016)
Chen, B.-Y.: Bergman kernel and hyperconvexity index. Anal. PDE 10, 1429–1454 (2017)
Demailly, J.-P., Kollár, J.: Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds. Ann. Scient. Éc. Norm. Sup. 34, 525–556 (2001)
Donnelly, H., Fefferman, C.: \(L^{2}\)-cohomology and index theorem for the Bergman metric. Ann. Math. 118, 593–618 (1983)
Guan, Q., Zhou, X.: Strong openness conjecture for plurisubharmonic functions. Ann. Math. 182, 605–616 (2015)
Hörmander, L.: Notions of Convexity. Birkhäuser (2007)
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Supported by NSF grant 11771089 and Grant IDH1411041 from Fudan University.
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Chen, BY. (2018). A Degenerate Donnelly–Fefferman Theorem and its Applications. In: Byun, J., Cho, H., Kim, S., Lee, KH., Park, JD. (eds) Geometric Complex Analysis. Springer Proceedings in Mathematics & Statistics, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-13-1672-2_6
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DOI: https://doi.org/10.1007/978-981-13-1672-2_6
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