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Numerical Computation of Surface Conformal Mappings

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Abstract

We report recent progress in the computation of conformal mappings from surfaces with arbitrary topologies to canonical domains. Two major computational methodologies are emphasized; one is holomorphic differentials based on Riemann surface theory and the other is surface Ricci flow from geometric analysis. The applications of surface conformal mapping in the field of engineering are briefly reviewed.

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Authors and Affiliations

  1. Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY, 11794, USA

    Xianfeng David Gu & Wei Zeng

  2. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854, USA

    Feng Luo

  3. Mathematics Department, Harvard University, Cambridge, MA, 02138, USA

    Shing-Tung Yau

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  1. Xianfeng David Gu
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  2. Wei Zeng
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  3. Feng Luo
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  4. Shing-Tung Yau
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Correspondence to Xianfeng David Gu.

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The research has been supported by NSF CCF-0448399, NSF DMS-0528363, NSF DMS-0626223, NSF IIS-0713145, NSF CCF-0830550, NSF CCF-0841514, ONR N000140910228, NSF III 0916286, NSF CCF-1081424, NSF Nets 1016829, NIH R01EB7530, and NSFC 60628202.

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Gu, X.D., Zeng, W., Luo, F. et al. Numerical Computation of Surface Conformal Mappings. Comput. Methods Funct. Theory 11, 747–787 (2012). https://doi.org/10.1007/BF03321885

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