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Results tagged with riemann-surfaces
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user 11142
Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.
1
vote
Accepted
Nielsen extension of Riemann surface
The below is a cut and paste from a paper from Noemi Goldberg, PAMS, 1986. I blame Preview for the typesetting quality (= not knowing about mathjax). However, the original poster could also have googl …
- 96.4k
1
vote
Universal covers of punctured hyperbolic surfaces
I strongly recommend you look at:
MR0795536 (86j:11069)
Series, Caroline(F-IHES)
The geometry of Markoff numbers.
Math. Intelligencer 7 (1985), no. 3, 20–29.
11J06 (11J13 11J70)
- 96.4k
1
vote
Dilatation of surface diffeomorphisms
The canonical reference is actually:
\bib{MR3134416}{article}{
author={McMullen, Curtis T.},
title={Entropy on Riemann surfaces and the Jacobians of finite covers},
journal={Comment. Math. He …
- 96.4k
3
votes
Can the limit set of an infinitely generated Schottky group have positive area?
Yes. This is due Z.-X. He, and in greater generality to Rich Schwartz, see
Schwartz, Richard, The limit sets of some infinitely generated Schottky groups, Trans. Am. Math. Soc. 335, No.2, 865-875 (19 …
- 96.4k
2
votes
Can the limit set of an infinitely generated Schottky group have positive area?
Almost surely such examples are constructed by Stratmann and Urbanski:
Stratmann, Bernd O.; Urba\'nski, Mariusz, Pseudo-Markov systems and infinitely generated Schottky groups, Am. J. Math. 129, No. …
- 96.4k
3
votes
Figure eight geodesic on a pair of pants/Y-piece
You are absolutely right, your method does the trick.
- 96.4k
1
vote
Why a non-simple geodesic in a Y-piece is NOT homotopic to a common perpendicular to the geo...
The thing about homotopies of curves is that they preserve the endpoints (on $S^1_\infty$) of the lifts. Whether or not two such lifts intersect depends only on the sign of the cross-ratio of the four …
- 96.4k
7
votes
What are the possible automorphism groups of Riemann surfaces of low genus?
The canonical reference on the subject (though one I don't have in front of me) is:
Characters and Automorphism Groups of Compact Riemann Surfaces
Part of London Mathematical Society Lecture Note Ser …
- 96.4k
1
vote
Does there exist a non-hyperelliptic Riemann surface with automorphism group $C_2\times A_4$?
There is a non-hyperelliptic (fixed-point free) involution of the surface of genus $5,$ with the quotient a surface of genus $3.$ Further, $A_4$ does come up as the automorphism group thereof, see
S. …
- 96.4k
0
votes
Embedding a Riemann surface in the sphere
Unless I am confused, why not add the points back, map the resulting surface to the Riemann sphere conformally by unifomization, then remove the images of the offending points?
- 96.4k
1
vote
A question on part of "An introduction to teichmuller spaces" by Imayoshi-Taniguchi
Here is the reference for Painleve's theorem:
http://eom.springer.de/p/p071100.htm (the second paragraph).
I don't understand your first question.
- 96.4k
2
votes
Accepted
Is every closed Sasakian 3-manifold a circle bundle on a Riemann surface?
A complete topological classification is due to Geiges, and can be found in this 2001 paper by Guilfoyle. (the first Theorem in the paper).
- 96.4k
3
votes
Accepted
Euclidean surfaces with conical singularities and cusped hyperbolic surfaces
Your description is a little too abstract: it is easier to think of this geometrically [in a special case].
Fact (Rivin, 1991): Every complete finite area hyperbolic metric on a sphere with punctures …
- 96.4k
4
votes
Complete metric on a Riemann surface with punctures
To see how you get complete metrics, you should know enough about hyperbolic geometry to know what an ideal triangle is. Once you do, note that any triangulation can be made of ideal triangles (usuall …
- 96.4k
11
votes
Accepted
Does every smoothly embedded surface $\mathbb{R}^3$ inherit a natural complex structure, and...
Question 1: Looks good to me.
Question 2: is a duplicate of this question (the answer is: every conformal structure can be so realized).
Question 3/4. There are algorithms to compute the conformal s …
- 96.4k