Inserted: 7 dec 2017
Last Updated: 16 jul 2019
Journal: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
We prove the second order differentiation formula along geodesics in finite-dimensional $RCD(K,N)$ spaces. Our approach strongly relies on the approximation of $W_2$-geodesics by entropic interpolations and, in order to implement this approximation procedure, on the proof of new (even in the smooth setting) estimates for such interpolations.