
Recent Posts
 StiefelWhitney cycles as intersections
 Schläfli – for lush, voluminous polyhedra
 Slightly elevated Teichmuller theory
 Mr Spock complexes (after Aitchison)
 Roots, Schottky semigroups, and Bandt’s Conjecture
 Taut foliations and positive forms
 Explosions – now in glorious 2D!
 Dipoles and Pixie Dust
 Mapping class groups: the next generation
 Groups quasiisometric to planes
 Div, grad, curl and all this
 A tale of two arithmetic lattices
 3manifolds everywhere
 kleinian, a tool for visualizing Kleinian groups
 Kähler manifolds and groups, part 2
 Kähler manifolds and groups, part 1
 Liouville illiouminated
 Scharlemann on Schoenflies
 You can solve the cube – with commutators!
 Chiral subsurface projection, asymmetric metrics and quasimorphisms
 Random groups contain surface subgroups
 wireframe, a tool for drawing surfaces
 Cube complexes, Reidemeister 3, zonohedra and the missing 8th region
 Orthocentricity
 Kenyon’s squarespirals
Blogroll
 0xDE
 Area 777
 Combinatorics and more
 Deep street soul
 Evaluating EDiscovery
 floerhomology
 Gaddeswarup
 Geometric Group Theory
 Godel's lost letter and P=NP
 Images des mathematiques
 Jim Woodring
 Language Log
 Letters of note
 Low dimensional topology
 Math Overflow
 Mathematics under the microscope
 nCategory Cafe
 Noncommutative geometry
 Paul Krugman
 Persiflage
 Preposterous Universe
 Questionable content
 Quomodocumque
 Real Climate
 Scott McCloud
 Secret blogging seminar
 Sketches of topology
 T Calegari
 Tanya Khovanova
 Terry Tao
 Tim Gowers
 Tony Phillips
Books
Software
Recent Comments
“A Teichmüller… on Slightly elevated Teichmuller… Herman Jaramillo on Hyperbolic Geometry Notes #2… SecretDoves on Random groups contain surface… Anton Izosimov on How to see the genus S^3 (the most basic… on Scharlemann on Schoenflies Categories
 3manifolds (20)
 4manifolds (2)
 Algebraic Geometry (2)
 Algebraic Topology (1)
 Biology (2)
 Commentary (4)
 Complex analysis (11)
 Convex geometry (2)
 Diophantine approximation (1)
 Dynamics (13)
 Ergodic Theory (8)
 Euclidean Geometry (8)
 Foliations (2)
 Geometric structures (6)
 Groups (31)
 Hyperbolic geometry (25)
 Knot theory (1)
 Lie groups (8)
 Number theory (2)
 Overview (2)
 Polyhedra (3)
 Probability (1)
 Projective geometry (2)
 Psychology (3)
 Riemannian geometry (1)
 Rigidity (2)
 Special functions (2)
 Surfaces (20)
 Symplectic geometry (3)
 TQFT (1)
 Uncategorized (5)
 Visualization (10)
Meta
Category Archives: Complex analysis
Slightly elevated Teichmuller theory
Last week at my invitation, David Dumas spoke in the U Chicago geometry seminar and gave a wonderful introductory talk on the theory of convex real projective structures on surfaces. This is the first step on the road to what is colloquially known … Continue reading
Dipoles and Pixie Dust
The purpose of this blog post is to give a short, constructive, computationfree proof of the following theorem: Theorem: Every compact subset of the Riemann sphere can be arbitrarily closely approximated (in the Hausdorff metric) by the Julia set of … Continue reading
Groups quasiisometric to planes
I was saddened to hear the news that Geoff Mess recently passed away, just a few days short of his 54th birthday. I first met Geoff as a beginning graduate student at Berkeley, in 1995; in fact, I believe he gave the … Continue reading
Kähler manifolds and groups, part 2
In this post I hope to start talking in a bit more depth about the global geometry of compact Kähler manifolds and their covers. Basic references for much of this post are the book Fundamental groups of compact Kähler manifolds by … Continue reading
Kähler manifolds and groups, part 1
One of the nice things about living in Hyde Park is the proximity to the University of Chicago. Consequently, over the summer I came in to the department from time to time to work in my office, where I have … Continue reading
Liouville illiouminated
A couple of weeks ago, my student Yan Mary He presented a nice proof of Liouville’s theorem to me during our weekly meeting. The proof was the one from BenedettiPetronio’s Lectures on Hyperbolic Geometry, which in my book gets lots … Continue reading
Posted in Complex analysis, Euclidean Geometry, Rigidity
Tagged conformal map, Liouville's theorem, Rigidity, umbilical surface
7 Comments