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Characterizing isolated singularities of conformal hyperbolic metrics

Funds:  Supported by NNSF of China(11931009, 11971450), Anhui Initiative in Quantum Information Technologies (AHY150200), the Fundamental Research Funds for the Central Universities.
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https://doi.org/10.3969/j.issn.0253-2778.2020.02.001
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  • Author Bio:

    FENG Yu, male, born in 1990, PhD candidate. Research field:Differential geometry. E-mail: yuf@mail.ustc.edu.cn

  • Corresponding author: XU Bin
  • Received Date: 02 December 2019
  • Accepted Date: 10 February 2020
  • Rev Recd Date: 10 February 2020
  • Publish Date: 28 February 2020
    Abstract

  • Abstract

    The explicit local models were classified for isolated singularities of complex one-dimensional hyperbolic metrics by complex analysis, which is interesting in its own way and could potentially be extended to higher dimensional cases.

    Abstract

    The explicit local models were classified for isolated singularities of complex one-dimensional hyperbolic metrics by complex analysis, which is interesting in its own way and could potentially be extended to higher dimensional cases.
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    • References(12)
  • [1]
    NITSCHE J. ber die isolierten singularitten der Lsungen von Δu = eu[J]. Math Z, 1957, 68: 316-324.
    [2]
    HEINS M. On a class of conformal metrics[J]. Nagoya Math J, 1962, 21: 1-60.
    [3]
    CHOU K S, WAN T. Asymptotic radial symmetry for solutions of Δu+eu=0 in a punctured disc[J]. Pacific Journal of Mathematics， 1994,163: 269-276.
    [4]
    CHOU K S, WAN T. Correction to “Asymptotic radial symmetry for solutions of Δu+eu=0 in a punctured disc”[J]. Pacific Journal of Mathematics, 1995, 171: 589-590.
    [5]
    YAMADA A. Bounded analytic functions and metrics of constant curvature of Riemann surfaces[J]. Kodai Math J, 1988, 11: 317-324.
    [6]
    LI B, FENG Y, LI L, et al. Bounded projective functions and hyperbolic metrics with isolated singularities[J].Annales Academiae Scientiarum Fennicae: Mathematica, 2020, 45: 687-698.
    [7]
    FENG Y, SHI Y Q, XU B. Isolated singularities of conformal hyperbolic metrics[J]. Chinese Annals of Mathematics, 2019, 40: 15-26(in Chinese)；Chinese J Contemp Math, 2019, 40: 15-26（English translation）.
    [8]
    RATCLIFFE J G. Foundations of Hyperbolic Manifolds[M]. 2nd ed. New York: Springer Science, 2006.
    [9]
    ANDERSON J W. Hyperbolic Geometry[M]. 2nd ed. London: Springer-Verlag, 2005.
    [10]
    BEARDON A F. The Geometry of Discrete Groups[M]. New York: Springer-Verlag, 1983.
    [11]
    AHLFORS L V. Complex Analysis[M]. 3rd ed. New York: McGraw-Hill, 1979.
    [12]
    STEIN E M, SHAKARCHI R. Complex Analysis[M]. Princeton, NJ: Princeton University Press, 2003.)
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    [1]
    NITSCHE J. ber die isolierten singularitten der Lsungen von Δu = eu[J]. Math Z, 1957, 68: 316-324.
    [2]
    HEINS M. On a class of conformal metrics[J]. Nagoya Math J, 1962, 21: 1-60.
    [3]
    CHOU K S, WAN T. Asymptotic radial symmetry for solutions of Δu+eu=0 in a punctured disc[J]. Pacific Journal of Mathematics， 1994,163: 269-276.
    [4]
    CHOU K S, WAN T. Correction to “Asymptotic radial symmetry for solutions of Δu+eu=0 in a punctured disc”[J]. Pacific Journal of Mathematics, 1995, 171: 589-590.
    [5]
    YAMADA A. Bounded analytic functions and metrics of constant curvature of Riemann surfaces[J]. Kodai Math J, 1988, 11: 317-324.
    [6]
    LI B, FENG Y, LI L, et al. Bounded projective functions and hyperbolic metrics with isolated singularities[J].Annales Academiae Scientiarum Fennicae: Mathematica, 2020, 45: 687-698.
    [7]
    FENG Y, SHI Y Q, XU B. Isolated singularities of conformal hyperbolic metrics[J]. Chinese Annals of Mathematics, 2019, 40: 15-26(in Chinese)；Chinese J Contemp Math, 2019, 40: 15-26（English translation）.
    [8]
    RATCLIFFE J G. Foundations of Hyperbolic Manifolds[M]. 2nd ed. New York: Springer Science, 2006.
    [9]
    ANDERSON J W. Hyperbolic Geometry[M]. 2nd ed. London: Springer-Verlag, 2005.
    [10]
    BEARDON A F. The Geometry of Discrete Groups[M]. New York: Springer-Verlag, 1983.
    [11]
    AHLFORS L V. Complex Analysis[M]. 3rd ed. New York: McGraw-Hill, 1979.
    [12]
    STEIN E M, SHAKARCHI R. Complex Analysis[M]. Princeton, NJ: Princeton University Press, 2003.)
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