Abstract
In this paper, we consider and resolve a geometric problem by using μ(z)-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that aC 1-two-real-dimensional connected orientable manifold with almost positive definite metric can be made into a Riemann surface by the method of isothermal coordinates. The result obtained here is actually a generalization of Chern’s work in 1955.
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Project (No. 10101023) supported by the National Natural Science Foundation of China
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Zhi-guo, C. Riemann surface with almost positive definite metric. J Zheijang Univ Sci A 6, 747–749 (2005). https://doi.org/10.1631/jzus.2005.A0747
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DOI: https://doi.org/10.1631/jzus.2005.A0747