Entire function invariant by translation is constant
7878
Proving that a doubly-periodic entire function $f$ is constant.
34223
Prove that every function that verifies $|f(x)-f(y)|\leq(x-y)^2$ for all $x,y$ is constant.
56978
How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?
39386
Harmonic non-surjective functions are constant
3818
Proving two entire functions are constant.
120533
A harmonic function with sublinear growth at infinity is constant
147516
Continuous function whose right hand derivative equals 0 is constant?
71479
Is there some elementary proof of invariance of domain?
31736
Removable singularities and an entire function
59409
Show Laplace operator is rotationally invariant
7755
Question on entire function
23615
Why does zero derivative imply a function is locally constant?
40208
Locally Constant Functions on Connected Spaces are Constant
74245
Characterizing non-constant entire functions with modulus $1$ on the unit circle
8805
Bounded linear operators that commute with translation
157322
Translation invariant measures on $\mathbb R$.
28399
Showing $f$ is constant