Geodesics in the space of $m$-subharmonic functions with bounded energy
Complex Variables
2021-10-07 v1 Differential Geometry
Metric Geometry
Abstract
With inspiration from the K\"ahler geometry, we introduce a metric structure on the energy class, , of -subharmonic functions with bounded energy and show that it is complete. After studying how the metric convergence relates to the accepted convergences in this Caffarelli-Nirenberg-Spruck model, we end by constructing geodesics in a subspace of our complete metric space.
Keywords
Cite
@article{arxiv.2110.02604,
title = {Geodesics in the space of $m$-subharmonic functions with bounded energy},
author = {Per Ahag and Rafal Czyz},
journal= {arXiv preprint arXiv:2110.02604},
year = {2021}
}