  We discuss c-functions and their holographic counterpart for two-dimensional
field theories with Carrollian conformal fixed points in the UV and the IR.
Specifically, we construct asymptotically flat domain wall solutions of
three-dimensional Einstein-dilaton gravity that model holographic RG flows
between BMS3 invariant UV and IR fixed points. We prove three theorems for such
flows: 1. for every holographic RG flow in AdS3, there is a corresponding one
in flat space, 2. the BMS central charge in the UV cannot be smaller than in
the IR, and 3. the UV/IR ratio of Virasoro central charges is identical to the
UV/IR ratio of corresponding BMS central charges. Finally, we tentatively
propose a Casini-Huerta-like c-functions for BMS3-invariant quantum field
theories, inspired by the AdS3/CFT2 relation between monotonicity of the
c-function and the quantum null energy condition.
