A general splitting principle on the non-smooth setting and applications

The thesis focuses on splitting-type theorems in RCD spaces. I and professor Nicola Gigli proved that if in an RCD space there exists a function with good gradient, Laplacian and Hessian then the space is isomorphic as metric measure space to a warped product space between the real line R and a space X'. Moreover we use this general result to prove two rigidity theorems (due to Li and Wang in the smooth setting) in case the space has positive spectrum of the Laplacian.