Gamma-convergence of Cheeger energies with respect to increasing distances

TL;DR

This paper establishes a gamma-convergence result for Cheeger energies in metric measure spaces with increasing distances, demonstrating the stability of the infinitesimal Hilbertianity condition under such convergence.

Contribution

It proves gamma-convergence of Cheeger energies with respect to increasing distances and shows the stability of infinitesimal Hilbertianity in this setting.

Findings

Gamma-convergence of Cheeger energies under increasing distances.

Stability of infinitesimal Hilbertianity condition.

Applicability to sequences of metric measure spaces.

Abstract

We prove a $\Gamma$-convergence result for Cheeger energies along sequences of metric measure spaces, where the measure space is kept fixed, while distances are monotonically converging from below to the limit one. As a consequence, we show that the infinitesimal Hilbertianity condition is stable under this kind of convergence of metric measure spaces.