Abstract: We extend are systematic analysis of holographic RG Flows to the QFTs defined on constant curvature manifolds.
The local and global properties of the flows are established. Non-trivial examples of skipping flows are analysed.
They exhibit exotic properties as well as examples of pure vev flows at finite curvature both by relevant and irrelevant operators.
The on-shell action on the sphere is systematically computed and analyzed.
It is found that it is related to the de Sitter entaglement entropy.
An systematic analysis of UV and IR divergences leads to several candidate F-functions in 3 dimensions, that are analyzed in detail.
The implications for F-theorems are discussed.