Leray-Schauder degree for the resonant Q-curvature problem in even dimensions
Abstract
In this paper, using the theory of critical points at infinity of Bahri, we derive an exact bubbling rate formula for the resonant prescribed Q-curvature equation on closed even-dimensional Riemannian manifolds. Using this, we derive new existence results for the resonant prescribed Q-curvature problem under a positive mass type assumption. Moreover, we derive a compactness theorem for conformal metrics with prescribed Q-curvature under a non-degeneracy assumption. Furthermore, combining the bubbling rate formula with the construction of some blowing-up solutions, we compute the Leray-Schauder degree of the resonant prescribed Q-curvature equation under a non-degeneracy and Morse type assumption.
Keywords
Cite
@article{arxiv.2206.12964,
title = {Leray-Schauder degree for the resonant Q-curvature problem in even dimensions},
author = {Cheikh Birahim Ndiaye},
journal= {arXiv preprint arXiv:2206.12964},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:1409.7919, arXiv:2107.12608, arXiv:1604.03745