Prescribing Morse scalar curvatures: blow-up analysis
Analysis of PDEs
2020-01-27 v2
Abstract
We study finite-energy blow-ups for prescribed Morse scalar curvatures in both the subcritical and the critical regime. After general considerations on Palais-Smale sequences we determine precise blow up rates for subcritical solutions: in particular the possibility of tower bubbles is excluded in all dimensions. In subsequent papers we aim to establish the sharpness of this result, proving a converse existence statement, together with a one to one correspondence of blowing-up subcritical solutions and {\em critical points at infinity}. This analysis will be then applied to deduce new existence results for the geometric problem.
Keywords
Cite
@article{arxiv.1812.09457,
title = {Prescribing Morse scalar curvatures: blow-up analysis},
author = {Andrea Malchiodi and Martin Mayer},
journal= {arXiv preprint arXiv:1812.09457},
year = {2020}
}
Comments
52 pages