In this paper, we consider the automorphisms of fine curve graphs where the vertices are restricted to continuously k k -differentiable curves. We show that for closed surfaces with genus at least 2, they are all induced by homeomorphisms of the surface. This result extends analogous work of Farb–Margalit and Long–Margalit–Pham–Verberne–Yao.
Katherine Williams Booth (Wed,) studied this question.