Computational Methods and Function Theory 11 (2011), No. 2, 747--787
Copyright Heldermann Verlag 2011
Xianfeng David Gu
gu@cs.sunysb.edu , State University of New York at Stony Brook, Department of Computer Science, Stony Brook, NY 11794, U.S.A.
Wei Zeng
zengwei@cs.sunysb.edu , State University of New York at Stony Brook, Department of Computer Science, Stony Brook, NY 11794, U.S.A.
Feng Luo
fluo@math.rutgers.edu , Rutgers University, Department of Mathematics, Piscataway, NJ 08854, U.S.A.
Shing-Tung Yau
yau@math.harvard.edu , Harvard University, Mathematics Department, Cambridge, MA 02138, U.S.A.
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.
Keywords: Conformal geometry, Ricci flow, holomorphic differential, discrete surface.
MSC 2000: Primary 53A30; Secondary 52C26.
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