Calculus of Variations and Geometric Measure Theory

N. Gigli - L. Tamanini

Second order differentiation formula on $RCD(K,N)$ spaces

created by tamanini1 on 07 Dec 2017
modified on 11 Sep 2023



Inserted: 7 dec 2017
Last Updated: 11 sep 2023

Journal: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
Year: 2018


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.