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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2005, Vol. 6 Issue ( 7): 23-    DOI: 10.1631/jzus.2005.A0747
    
Riemann surface with almost positive definite metric*
CHEN Zhi-guo
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
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Abstract  In this paper, we consider and resolve a geometric problem by using m(z)-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that a C1-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?ˉs work in 1955.

Key words： Mathematic Quasiconformal mapping      μ(z)-homeomorphisms      Beltrami equation      Isothermal coordinates     
Received: 08 November 2004     
CLC:  O174.5  
  O186  
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CHEN Zhi-guo. Riemann surface with almost positive definite metric*. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 7): 23-.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2005.A0747     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2005/V6/I 7/23

[1] Chen Zhi-Guo. A problem on extremal quasiconformal extensions[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(Supplement 2): 198-202.
[2] Chen Zhi-Guo. A problem on extremal quasiconformal extensions[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 0, (): 198-202.