Higher order Bol's inequality and its applications
Differential Geometry
2024-04-19 v2 Analysis of PDEs
Abstract
In the conformal class of Euclidean space, we give some volume comparison theorems with help of Q-curvature. Meanwhile, for compact four dimensional manifolds with non-negative scalar curvature, we give a volume rigidity theorem with respect to Q-curvature. Finally, we make use of these results to give some sufficient and necessary conditions for the existence of solutions to some conformally invariant equations which answers an open problem raised by Hyder-Martinazzi (2021, JDE).
Cite
@article{arxiv.2308.11388,
title = {Higher order Bol's inequality and its applications},
author = {Mingxiang Li and Juncheng Wei},
journal= {arXiv preprint arXiv:2308.11388},
year = {2024}
}
Comments
26 pages. New version