Question

Is this a valid conformal map for my problem?

score 82 · Answer 1 · 2021-08-13 21:18:46

82

Views

Is this a valid conformal map for my problem?

Published on 13 Aug 2021 - 21:18

score 57 · Answer 2 · 2021-08-16 17:07:29

57

Views

How to show directly that $T(G \setminus \{a\})$ is open?

Published on 16 Aug 2021 - 17:07

score 184 · Answer 3 · 2021-08-21 08:59:07

184

Views

Finding a Möbius transformation sending a set onto the open unit disk.

Published on 21 Aug 2021 - 8:59

score 66 · Answer 4 · 2021-08-27 12:19:29

66

Views

If $f$ is holomorphic in $D = \Bbb D\cap\{\Re(z)>0\}$, $f(a)=a$ for $a\in D$ and $f(D)\subset D$, how to show that $|f'(a)|\le 1$?

Published on 27 Aug 2021 - 12:19

score 536 · Answer 5 · 2021-09-06 07:32:24

536

Views

Is a rational function which maps all circles/lines to circles/lines a Möbius transformation?

Published on 06 Sep 2021 - 7:32

score 241 · Answer 6 · 2021-10-05 21:40:16

241

Views

Show that every element of $\text{Mob}^+(\mathbb{H})$ is the product of two inversions.

Published on 05 Oct 2021 - 21:40

score 49 · Answer 7 · 2021-10-06 18:44:20

49

Views

Determine for which pairs $\eta, \lambda > 0$ the mappings $h_\eta, h_\lambda$ are conjugate in $\text{Mob}(\mathbb{H)}$.

Published on 06 Oct 2021 - 18:44

score 51 · Answer 8 · 2021-10-20 15:54:51

51

Views

Find Möbius Transformation over an annulus

Published on 20 Oct 2021 - 15:54

score 29 · Answer 9 · 2021-10-24 23:06:44

29

Views

Prove conjecture about classification of circle pairings

Published on 24 Oct 2021 - 23:06

score 343 · Answer 10 · 2021-10-27 00:05:02

343

Views

Show that any biholomorphic map from the upper half plane to itself is a Mobius transform

Published on 27 Oct 2021 - 0:05

score 89 · Answer 11 · 2021-11-02 07:20:43

89

Views

prove a property for the stabiliser of 0 by the map apply action of a discrete subgroup of Aut(D)

Published on 02 Nov 2021 - 7:20

score 198 · Answer 12 · 2021-11-26 23:35:03

198

Views

Proof that the composition of two inversion with the same center is a homothety

Published on 26 Nov 2021 - 23:35

score 621 · Answer 13 · 2021-12-07 16:49:38

621

Views

Explicitly representing an isometry as a composition of circle inversions

Published on 07 Dec 2021 - 16:49

score 250 · Answer 14 · 2021-12-14 18:10:08

250

Views

Show that the Möbius group (or general linear projective space $PGL(2,\mathbb{C})$) is not simply connected.

Published on 14 Dec 2021 - 18:10

score 365 · Answer 15 · 2021-12-18 17:13:27

365

Views

Find a Möbius transformation such that a semi-circle in the upper half plane is mapped to $i\mathbb{R}_{>0}$

Published on 18 Dec 2021 - 17:13

List Question

Is this a valid conformal map for my problem?

How to show directly that $T(G \setminus \{a\})$ is open?

Finding a Möbius transformation sending a set onto the open unit disk.

If $f$ is holomorphic in $D = \Bbb D\cap\{\Re(z)>0\}$, $f(a)=a$ for $a\in D$ and $f(D)\subset D$, how to show that $|f'(a)|\le 1$?

Is a rational function which maps all circles/lines to circles/lines a Möbius transformation?

Show that every element of $\text{Mob}^+(\mathbb{H})$ is the product of two inversions.

Determine for which pairs $\eta, \lambda > 0$ the mappings $h_\eta, h_\lambda$ are conjugate in $\text{Mob}(\mathbb{H)}$.

Find Möbius Transformation over an annulus

Prove conjecture about classification of circle pairings

Show that any biholomorphic map from the upper half plane to itself is a Mobius transform

prove a property for the stabiliser of 0 by the map apply action of a discrete subgroup of Aut(D)

Proof that the composition of two inversion with the same center is a homothety

Explicitly representing an isometry as a composition of circle inversions

Show that the Möbius group (or general linear projective space $PGL(2,\mathbb{C})$) is not simply connected.

Find a Möbius transformation such that a semi-circle in the upper half plane is mapped to $i\mathbb{R}_{>0}$

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