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 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’s work in 1955.

Key words: Quasiconformal mapping, μ(z)-homeomorphisms, Beltrami equation, Isothermal coordinates

Please provide your name, email address and a comment

Your Name: Affili: E-Mail Address:

Comment (Please comment in English):


Verification Code(click to change a pic):