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 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).
- Publication:
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arXiv e-prints
- Pub Date:
- August 2023
- DOI:
- 10.48550/arXiv.2308.11388
- arXiv:
- arXiv:2308.11388
- Bibcode:
- 2023arXiv230811388L
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Analysis of PDEs;
- 53C18;
- 35A23
- E-Print:
- 26 pages. New version