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 on 24 Jan 2020



Inserted: 22 dec 2018
Last Updated: 24 jan 2020

Pages: 53
Year: 2018

To appear on I.M.R.N.


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.