Higher order Bol's inequality and its applications
Abstract
In the conformal class of Euclidean space, we give some volume comparison theorems with help of Qcurvature. Meanwhile, for compact four dimensional manifolds with nonnegative scalar curvature, we give a volume rigidity theorem with respect to Qcurvature. 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 HyderMartinazzi (2021, JDE).
 Publication:

arXiv eprints
 Pub Date:
 August 2023
 DOI:
 10.48550/arXiv.2308.11388
 arXiv:
 arXiv:2308.11388
 Bibcode:
 2023arXiv230811388L
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs;
 53C18;
 35A23
 EPrint:
 26 pages. New version