I would say holomorphic everywhere, injective and bijective only in $D=\mathbb{R}\times [-\pi,\pi]$, so also only biholomorph in that D.
Is that true? Are there alternatives?
I would say holomorphic everywhere, injective and bijective only in $D=\mathbb{R}\times [-\pi,\pi]$, so also only biholomorph in that D.
Is that true? Are there alternatives?