Metric compatibility and determination in complete metric spaces
Abstract
It was established in [8] that Lipschitz inf-compact functions are uniquely determined by their local slope and critical values. Compactness played a paramount role in this result, ensuring in particular the existence of critical points. We hereby emancipate from this restriction and establish a determination result for merely bounded from below functions, by adding an assumption controlling the asymptotic behavior. This assumption is trivially fulfilled if is inf-compact. In addition, our result is not only valid for the (De Giorgi) local slope, but also for the main paradigms of average descent operators as well as for the global slope, case in which the asymptotic assumption becomes superfluous. Therefore, the present work extends simultaneously the metric determination results of [8] and [18].
Keywords
Cite
@article{arxiv.2308.14877,
title = {Metric compatibility and determination in complete metric spaces},
author = {Aris Daniilidis and Tri Minh Le and David Salas},
journal= {arXiv preprint arXiv:2308.14877},
year = {2023}
}