Transformation of  p -gradient flows to  p ′-gradient flows in metric spaces

We explicitly construct parameter transformations between gradient flows in metric spaces, called curves of maximal slope, having different exponents when the associated function and the associated metric space satisfy a suitable convexity condition. These transformations induce the existence of canonical bijective maps between gradient flows. We also prove the regularizing effects of gradient flows. To establish these results, we work directly with gradient flows instead of using variational discrete approximations which are often used in the study of gradient flows.