Calculus of Variations and Geometric Measure Theory

A. Malchiodi - M. Mayer

Prescribing Morse scalar curvatures: blow-up analysis

created by malchiodi on 22 Dec 2018
modified by mayer1 on 23 Jul 2026

[BibTeX]

Published Paper

Inserted: 22 dec 2018
Last Updated: 23 jul 2026

Pages: 53
Year: 2018
Doi: https://doi.org/10.1093/imrn/rnaa021

ArXiv: 1812.09457 PDF

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.


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