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1
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1answer
199 views

Conformal extension

Does there exist a conformal smooth extension of a smooth function? Smooth extension is guaranteed by Whitney extension theorem. does that theorem also says for conformality. Precisely the ...
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2answers
211 views

general conformal transf. extension to hyperbolic manifold

I have an hyperbolic manifold with boundary a conformal sphere. Can I extend any conformal transformation of boundary to the interior of the ball? I know how to do with Moebius but I wonder if there ...
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1answer
830 views

Geometric Interpretation of $Q$-curvature

Let $(M,g)$ be a Riemannian manifold of dimension $n>2$. Thanks to the late T.Branson we have the following definition of the so-called $Q$-curvature: $Q= \Delta R + ...
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2answers
331 views

Approximation of conformal mapping as a sum of elementary conformal mappings

Hi, I would like to approximate any 2d conformal mapping, as a sum of elementary conformal mappings. So I would have some basis, a conformal mapping with some parameters, and by adding several ones ...
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0answers
290 views

Collection of charged line segments in 2D - where do electric field lines meet it?

Suppose we have a collection of charged line segments in 2D. I'd like to be able to do two things : from an arbitrary point in the plane, follow the electric field and find where it meets the ...
11
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3answers
616 views

Conformal Welding Reference

I'm looking for a reference for the following fact: given two Riemann surfaces and an identification of their boundaries, once I topologically glue the surfaces together there exists a unique ...
4
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3answers
736 views

Conformal-symplectic geometry ?

I think in priciple it's possible to consider a theory of "conformal-symplectic manifolds", in an analogous fashion as the usual conformal geometry. To spell out the spontaneous definitions: say ...
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1answer
1k views

Is there a manifold structure on a space of conformal maps?

I would be very grateful for any information or pointers for the following: 1) Fix an open subset $U$ of $\mathbb{CP}^1$. a) Does the set of all holomorphic maps from $U$ to $\mathbb{C}$ (with the ...
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0answers
249 views

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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1answer
484 views

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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2answers
2k views

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 ...
6
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1answer
480 views

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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5answers
2k views

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 ...