Question

Let $h(z) = g(f(z))$. If $f$ and $h$ are non-constant holomorphic function on domains in $\mathbb C^n$, then is $g$ holomorphic?

score 51 · Answer 1 · 2026-03-22 17:57:21

Let $h(z) = g(f(z))$. If $f$ and $h$ are non-constant holomorphic function on domains in $\mathbb C^n$, then is $g$ holomorphic?

score 170 · Answer 2 · 2026-03-22 21:14:56

170

Views

If power series in two variables and logarithmically convex Reinhardt domains

Published on 22 Mar 2026 - 21:14

score 120 · Answer 3 · 2026-03-20 07:54:45

120

Views

Product of holomorphically convex spaces is again holomorphically convex

Published on 20 Mar 2026 - 7:54

score 609 · Answer 4 · 2026-03-23 07:17:14

609

Views

Differential Geometry tools in Several Complex Variables

Published on 23 Mar 2026 - 7:17

score 440 · Answer 5 · 2026-03-20 03:49:09

440

Views

Is the complement of a complex affine algebraic set in an irreducible complex affine algebraic set (path) connected in the euclidean topology?

Published on 20 Mar 2026 - 3:49

score 232 · Answer 6 · 2026-03-23 02:46:57

232

Views

Any entire holomorphic function that is bounded on countably infinite number of complex-lines must be constant.

Published on 23 Mar 2026 - 2:46

score 111 · Answer 7 · 2026-03-20 03:26:42

111

Views

Do there exist infinitely many complex lines through the origin?

Published on 20 Mar 2026 - 3:26

score 100 · Answer 8 · 2026-03-23 08:12:38

100

Views

Can a pure codimension d analytic subset be defined by a d-tuple of holomorphic functions?

Published on 23 Mar 2026 - 8:12

score 1.1k · Answer 9 · 2026-03-23 02:27:18

1.1k

Views

How to show $\int_{0}^{\infty} \frac{dx}{x^3+1} = \frac{2\pi}{3\sqrt{3}}$

Published on 23 Mar 2026 - 2:27

score 201 · Answer 10 · 2026-03-22 22:29:49

201

Views

Build a Blaschke product such as $B^*(1)=\lim_{r\to 1}B(r)=0$

Published on 22 Mar 2026 - 22:29

score 135 · Answer 11 · 2026-03-23 11:05:19

135

Views

$C^{k}$ topologies on $ Hol(U)$

Published on 23 Mar 2026 - 11:05

score 185 · Answer 12 · 2026-03-22 11:41:44

185

Views

Prove that every complex number with modulus 1 can be expressed as the principal value $(−1)^a$ for some real number a.

Published on 22 Mar 2026 - 11:41

score 106 · Answer 13 · 2026-03-22 04:01:32

106

Views

Almost everywhere equal plurisubharminic functions

Published on 22 Mar 2026 - 4:01

score 123 · Answer 14 · 2026-03-22 04:04:38

123

Views

$C^3$ boundary, locally the Levi form satisfies $L(r,t)\geq -C|r(z)||t|^2$ for tangent vectors $t$ and defining function $r$.

Published on 22 Mar 2026 - 4:04

score 191 · Answer 15 · 2026-03-21 18:31:03

191

Views

Holomorphic logarithm of a never-zero holomorphic function on balls in $\mathbb C^n$

Published on 21 Mar 2026 - 18:31

List Question

Let $h(z) = g(f(z))$. If $f$ and $h$ are non-constant holomorphic function on domains in $\mathbb C^n$, then is $g$ holomorphic?

If power series in two variables and logarithmically convex Reinhardt domains

Product of holomorphically convex spaces is again holomorphically convex

Differential Geometry tools in Several Complex Variables

Is the complement of a complex affine algebraic set in an irreducible complex affine algebraic set (path) connected in the euclidean topology?

Any entire holomorphic function that is bounded on countably infinite number of complex-lines must be constant.

Do there exist infinitely many complex lines through the origin?

Can a pure codimension d analytic subset be defined by a d-tuple of holomorphic functions?

How to show $\int_{0}^{\infty} \frac{dx}{x^3+1} = \frac{2\pi}{3\sqrt{3}}$

Build a Blaschke product such as $B^*(1)=\lim_{r\to 1}B(r)=0$

$C^{k}$ topologies on $ Hol(U)$

Prove that every complex number with modulus 1 can be expressed as the principal value $(−1)^a$ for some real number a.

Almost everywhere equal plurisubharminic functions

$C^3$ boundary, locally the Levi form satisfies $L(r,t)\geq -C|r(z)||t|^2$ for tangent vectors $t$ and defining function $r$.

Holomorphic logarithm of a never-zero holomorphic function on balls in $\mathbb C^n$

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