Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902432 | Journal de Mathématiques Pures et Appliquées | 2018 | 32 Pages |
Abstract
We study a transformation of metric measure spaces introduced by Gigli and Mantegazza consisting in replacing the original distance with the length distance induced by the transport distance between heat kernel measures. We study the smoothing effect of this procedure in two important examples. Firstly, we show that in the case of particular Euclidean cones, a singularity persists at the apex. Secondly, we generalize the construction to a sub-Riemannian manifold, namely the Heisenberg group, and show that it regularizes the space instantaneously to a smooth Riemannian manifold.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Matthias Erbar, Nicolas Juillet,