Skip to main content

Revisiting a Non-Degeneracy Property for Extremal Mappings

Acta Mathematica Scientia volume 41, pages 1829–1838 (2021)Cite this article

Abstract

We extend an earlier result obtained by the author in [7].

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. Abate M. Iteration Theory of Holomorphic Maps on Taut Manifolds. Rende, Cosenza: Mediterranean Press, 1989

    MATH  Google Scholar 

  2. Baracco L, Zaitsev D, Zampieri G. A Burns-Krantz type theorem for domains with corners. Math Ann, 2006, 336: 491–504

    MathSciNet  Article  Google Scholar 

  3. Bracci F, Patrizio G. Monge-Ampère foliations with singularities at the boundary of strongly convex domains. Math Ann, 2005, 332: 499–522

    MathSciNet  Article  Google Scholar 

  4. Bracci F, Patrizio G, Trapani S. The pluricomplex Poisson kernel for strongly convex domains. Trans Amer Math Soc, 2009, 361: 979–1005

    MathSciNet  Article  Google Scholar 

  5. Chang C H, Hu M C, Lee H P. Extremal analytic discs with prescribed boundary data. Trans Amer Math Soc, 1988, 310: 355–369

    MathSciNet  Article  Google Scholar 

  6. Huang X. A preservation principle of extremal mappings near a strongly pseudoconvex point and its applications. Illinois J Math, 1994, 38: 283–302

    MathSciNet  Article  Google Scholar 

  7. Huang X. A non-degeneracy property of extremal mappings and iterates of holomorphic self-mappings. Ann Scuola Norm Sup Pisa Cl Sci, 1994, 21: 399–419

    MathSciNet  MATH  Google Scholar 

  8. Huang X, Wang W. Complex geodesics and complex Monge-Ampére equations with boundary singularity. Math Ann, 2020 (in press)

  9. Lempert L. La métrique de Kobayashi et la représentation des domaines sur la boule. Bull Soc Math France, 1981, 109: 427–474

    MathSciNet  Article  Google Scholar 

  10. Lempert L. Intrinsic distances and holomorphic retracts//Complex Analysis and Applications’ 81 (Varna, 1981). Sofia: Publ House Bulgar Acad Sci, 1984: 341–364

    Google Scholar 

  11. Lempert L. A precise result on the boundary regularity of biholomorphic mappings. Math Z, 1986, 193: 559–579; Erratum, 1991, 206: 501–504

    MathSciNet  Article  Google Scholar 

  12. Poletsky E A. The Euler-Lagrange equations for extremal holomorphic mappings of the unit disk. Michigan Math J, 1983, 30: 317–333

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08903, USA

    Xiaojun Huang

Authors
  1. Xiaojun Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaojun Huang.

Additional information

Dedicated to the memory of Professor Jiarong YU

Partially supported by NSF grants DMS-1665412 and DMS-2000050.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Huang, X. Revisiting a Non-Degeneracy Property for Extremal Mappings. Acta Math Sci 41, 1829–1838 (2021). https://doi.org/10.1007/s10473-021-0602-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10473-021-0602-6

Key words

  • non-degeneracy property
  • extremal mapping
  • pseudoconvex

2010 MR Subject Classification

  • 32G07
  • 32F32