Prescribing Morse scalar curvatures: blow-up analysis
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2018
- DOI:
- 10.48550/arXiv.1812.09457
- arXiv:
- arXiv:1812.09457
- Bibcode:
- 2018arXiv181209457M
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- 52 pages