The total Q-curvature, volume entropy and polynomial growth polyharmonic functions (II)
Differential Geometry
2024-09-16 v2 Analysis of PDEs
Abstract
This is a continuation of our previous work (Advances in Mathematics 450 (2024), Paper No. 109768). In this paper, we characterize complete metrics with finite total Q-curvature as normal metrics for all dimensional cases. Secondly, we introduce another volume entropy to provide geometric information regarding complete non-normal metrics with finite total Q-curvature. In particular, we show that if the scalar curvature is bounded from below, the volume growth of such complete metrics is controlled.
Cite
@article{arxiv.2408.03640,
title = {The total Q-curvature, volume entropy and polynomial growth polyharmonic functions (II)},
author = {Mingxiang Li},
journal= {arXiv preprint arXiv:2408.03640},
year = {2024}
}
Comments
20 pages. Comments are welcome!