Talk:Beltrami equation
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Rewrite of Section 2
[edit]Section 2 discusses Gauss's technique for constructing isothermal coordinates for an analytic metric. User:Mathsci contributed that text in mid-2012. Motivated by a concrete problem of that type, I tried to figure out what that version of Section 2 was saying, but with no luck. I commented on my confusion on this Talk page, but with no response. After a while, I commented on my confusion also on the Talk page for the Mathematics project, but with no response to that either.
Recently, by going back to the referenced Volume IV of Spivak, I have figured out how Gauss's construction works. I have written up a cookbook for that construction as a new, longer version of Section 2.
There is some risk that the 2012 version of Section 2 had useful ideas in it, ideas that should not be lost. If some expert in the field finds this to be the case, I'd be happy to hear what those ideas are, and, once I understand them, to help in trying to incorporate them more clearly into either this page or some other Wikipedia page.