Title: On the uniqueness of complete biconservative surfaces in $\mathbb{R}^3$,
Abstract: We study the uniqueness of complete biconservative surfaces in the Euclidean
space $\mathbb{R}^3$, and prove that the only complete biconservative regular
surfaces in $\mathbb{R}^3$ are either $CMC$ or certain surfaces of revolution.
In particular, any compact biconservative regular surface in $\mathbb{R}^3$ is
a round sphere.