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Errata in “Conformal Mapping: Method and Applications” from Schinzinger

hi, i'm studying the book "Conformal Mapping: Method and Applications" from Schinzinger and more precisely the chapter 6 concerning non-planar field. In section 6.1.3 the author proposes to solve a ...
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Invariance of the cylindrical Laplace equation under conformal transform

hello, it is often said that a conformal mapping preserves the Laplace equetion in 2D. However, if this is true for the cartesian coordinates (x,y), where the laplacian is: $$ \frac{\partial^2 ...
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A question about the proof of Mostow rigidity

I have recently been studying a proof of Mostow rigidity (along the lines of Mostow's original argument), and I'm left a little confused about something. We start with an isomorphism $\alpha: \Gamma ...
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Analogy of Liouville conformal mapping theorem with Mostow rigidity?

I often hear mention of two theorems, Mostow's rigidity theorem and Liouville's theorem on conformal mappings, which superficially sound similar: they say that a set of geometric structures is, if ...
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Intuition behind moduli space of curves

For a genus g compact smooth surface $M$, an algebraic structure is the same as a complex structure is the same as a conformal structure. So the moduli space of smooth curves should be the same as the ...