Skip to main content

A Degenerate Donnelly–Fefferman Theorem and its Applications

  • Conference paper
  • First Online:

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 246))

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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. 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)

    Google Scholar 

  2. Berndtsson, B.: The openness conjecture for plurisubharmonic functions. arXiv:1305.5781

  3. Berndtsson, B., Charpentier, P.: A Sobolev mapping property of the Bergman kernel. Math. Z. 235, 1–10 (2000)

    Article  MathSciNet  Google Scholar 

  4. Blocki, Z.: Cauchy-Riemann meet Monge-Amp\(\grave{e}\)re. Bull. Math. Sci. 4, 433–480 (2014)

    Article  MathSciNet  Google Scholar 

  5. Chen, B.-Y.: A simple proof of the Ohsawa-Takegoshi extension theorem. arXiv:1105.2430v1

  6. Chen, B.-Y.: Parameter dependence of the Bergman kernels. Adv. Math. 299, 108–138 (2016)

    Article  MathSciNet  Google Scholar 

  7. Chen, B.-Y.: Bergman kernel and hyperconvexity index. Anal. PDE 10, 1429–1454 (2017)

    Article  MathSciNet  Google Scholar 

  8. 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)

    Article  Google Scholar 

  9. Donnelly, H., Fefferman, C.: \(L^{2}\)-cohomology and index theorem for the Bergman metric. Ann. Math. 118, 593–618 (1983)

    Article  MathSciNet  Google Scholar 

  10. Guan, Q., Zhou, X.: Strong openness conjecture for plurisubharmonic functions. Ann. Math. 182, 605–616 (2015)

    Article  MathSciNet  Google Scholar 

  11. Hörmander, L.: Notions of Convexity. Birkhäuser (2007)

    Google Scholar 

Download references

Acknowledgements

Supported by NSF grant 11771089 and Grant IDH1411041 from Fudan University.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bo-Yong Chen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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

Download citation

Publish with us

Policies and ethics