Question

If $f$ is injective on $B_r(z_0)$ and holomorphic on $\overline{B_r(z_0)} $, then $f(B_r(z_0))\cap f(\partial B_r(z_0) )=\emptyset$

score 48 · Answer 1 · 2018-09-28 07:35:01

48

Views

If $f$ is injective on $B_r(z_0)$ and holomorphic on $\overline{B_r(z_0)} $, then $f(B_r(z_0))\cap f(\partial B_r(z_0) )=\emptyset$

Published on 28 Sep 2018 - 7:35

score 74 · Answer 2 · 2026-03-25 09:28:58

74

Views

$f:D(0,1) \to \mathbb{C}$ holomorphic injective such that $f(0) = 1 = f'(0)$ and $f^{(k)}(0) \in \mathbb{R} \; \forall k$

Published on 25 Mar 2026 - 9:28

score 47 · Answer 3 · 2018-09-30 07:02:25

47

Views

Checking Holomorphicity of functions?

Published on 30 Sep 2018 - 7:02

score 1.9k · Answer 4 · 2018-10-01 10:03:25

1.9k

Views

Is there a holomorphic and bijective function of the unit disc onto the complex plane?

Published on 01 Oct 2018 - 10:03

score 1.2k · Answer 5 · 2026-03-25 03:06:58

1.2k

Views

Proving a holomorphic function is identically zero when its zeros form a sequence that converge in some region

Published on 25 Mar 2026 - 3:06

score 38 · Answer 6 · 2018-10-02 13:15:31

38

Views

Need help with proving/understanding uniform convergence of derivatives of analytic function. (Proof Verification)

Published on 02 Oct 2018 - 13:15

score 69 · Answer 7 · 2018-10-03 00:22:37

69

Views

Radius of convergence of a power series.

Published on 03 Oct 2018 - 0:22

score 122 · Answer 8 · 2026-03-25 23:39:35

122

Views

Find a harmonic function u that vanishes on C[0, 2] and satisfies $u(3e^{i\theta}) = 65\cos(2\theta)$

Published on 25 Mar 2026 - 23:39

score 56 · Answer 9 · 2018-10-09 02:38:54

56

Views

Contradiction for Roots of a Complex Polynomial?

Published on 09 Oct 2018 - 2:38

score 63 · Answer 10 · 2018-10-09 11:16:39

63

Views

Prove that $|f(z)-f(0)-f'(0)z|\leq f(|z|)-f(0)-f'(0)|z|$ on unit disc

Published on 09 Oct 2018 - 11:16

score 151 · Answer 11 · 2018-10-10 13:27:08

151

Views

Simply connected space and open mapping theorem

Published on 10 Oct 2018 - 13:27

score 278 · Answer 12 · 2018-10-12 17:52:40

278

Views

Proof that $f(z)/(z-a)$ is holomorphic if $f(z)$ is holomorphic

Published on 12 Oct 2018 - 17:52

score 369 · Answer 13 · 2018-10-12 18:02:20

369

Views

$w = \log z$ is analytic on $D = \{z : \alpha < \arg z < \alpha +2\pi k\}$

Published on 12 Oct 2018 - 18:02

score 21 · Answer 14 · 2018-10-14 13:56:48

If the derivatives of $f$ for $t\in L$ are real functions, then $f(\bar{z})=\overline{f(z)}, \forall z\in B(t,r).$

score 93 · Answer 15 · 2018-10-16 11:43:32

93

Views

Is there a holomorphic bijection from the left-hand side of the complex plane to the unit disk with this property?

Published on 16 Oct 2018 - 11:43

List Question

If $f$ is injective on $B_r(z_0)$ and holomorphic on $\overline{B_r(z_0)} $, then $f(B_r(z_0))\cap f(\partial B_r(z_0) )=\emptyset$

$f:D(0,1) \to \mathbb{C}$ holomorphic injective such that $f(0) = 1 = f'(0)$ and $f^{(k)}(0) \in \mathbb{R} \; \forall k$

Checking Holomorphicity of functions?

Is there a holomorphic and bijective function of the unit disc onto the complex plane?

Proving a holomorphic function is identically zero when its zeros form a sequence that converge in some region

Need help with proving/understanding uniform convergence of derivatives of analytic function. (Proof Verification)

Radius of convergence of a power series.

Find a harmonic function u that vanishes on C[0, 2] and satisfies $u(3e^{i\theta}) = 65\cos(2\theta)$

Contradiction for Roots of a Complex Polynomial?

Prove that $|f(z)-f(0)-f'(0)z|\leq f(|z|)-f(0)-f'(0)|z|$ on unit disc

Simply connected space and open mapping theorem

Proof that $f(z)/(z-a)$ is holomorphic if $f(z)$ is holomorphic

$w = \log z$ is analytic on $D = \{z : \alpha < \arg z < \alpha +2\pi k\}$

If the derivatives of $f$ for $t\in L$ are real functions, then $f(\bar{z})=\overline{f(z)}, \forall z\in B(t,r).$

Is there a holomorphic bijection from the left-hand side of the complex plane to the unit disk with this property?

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