# Questions tagged [quasiconformal-maps]

Quasiconformal maps are generalizations of conformal maps. They started out being used in Nevanlinna's value distribution theory but now form a fundamental component of geometric function theory. This tag is for questions related to QC maps.

83 questions
Filter by
Sorted by
Tagged with
32 views

35 views

129 views

### Is a holomorphic function with nonvanishing derivative almost injective?

Let $\Omega \subseteq \mathbb C$, be an open, bounded, connected, contractible subset with smooth boundary. Let $f:\Omega \to \mathbb C$ be holomorphic, and suppose that its derivative $f'$ is ...
296 views

27 views

### Derivatives at the zero point of a conformal map from the unit strip onto the unit disc

Let $w$ be a point in the unit strip $\mathbb{S}=\{z\in \mathbb{C} : 0< Re\, z<1\}$ and let $\phi_w$ be a conformal map from $\mathbb{S}$ onto the unit disc $\mathbb{D}$ with $\phi_w(w)=0$. It ...
266 views

49 views

### Find the form of $f:\mathbb{C}\to\mathbb{C}$ which is entire, conformal and $\lim_{z\to\infty} f(z)=\infty$

Find the most general form of a function $f:\mathbb{C}\to\mathbb{C}$ which is entire, conforal and $\lim_{z\to\infty} f(z)=\infty$. I know that if $f$ is entire and $\lim_{z\to\infty}f(z)=\infty$ ...
1 vote
31 views

96 views

### Finding a suitable transformation function for the picture

I haven't taken complex analysis yet so there may be many words to sift through and not much concrete mathematical notation. I'll try my best though. Given a local Euclidean unit square grid how ...
228 views

### Producing isothermal coordinates from a solution of the Beltrami Equation

Suppose that $f \colon U \to V$ is a diffeomorphism of planar domains. Its differential $Df$ can be pointwise expressed the sum of a complex-linear and complex-anti-linear mapping: Given a tangent ...
1 vote
2k views

### A special Mobius Transformation that maps the right half plane to the unit disc

Find the Mobius Transformation that maps the right half plane to the unit disc carrying the point $z=15$ to the origin. Since the Mobius transformation takes the point $z=15$ to the origin, so I ...
Let $f:M \to N$ be a smooth weakly conformal map between connected $d$-dimensional Riemannian manifolds, i.e. $f$ satisfies $df^Tdf =(\det df)^{\frac{2}{d}} \, \text{Id}$. Assume $d \ge 3$ and ...