Calculus of Variations and Geometric Measure Theory

A. Malchiodi - M. Mayer

Prescribing Morse scalar curvatures: pinching and Morse theory

created by malchiodi on 07 Sep 2019
modified on 19 May 2021



Inserted: 7 sep 2019
Last Updated: 19 may 2021

Journal: accepted on C.P.A.M.
Pages: 32
Year: 2019

Some corrections made in Section 4.


We consider the problem of prescribing conformally the scalar curvature on compact manifolds of positive Yamabe class in dimension $n \geq 5$. We prove new existence results using Morse theory and some analysis on blowing-up solutions, under suitable pinching conditions on the curvature function. We also provide new non-existence results showing the sharpness of some of our assumptions, both in terms of the dimension and of the Morse structure of the prescribed function.