Prescribing Morse scalar curvatures: pinching and Morse theory

Abstract

We consider the problem of prescribing conformally the scalar curvature on compact manifolds of positive Yamabe class in dimension $n\ge 5$. 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.

References in corpus (3)

• Prescribing Morse scalar curvatures: subcritical blowing-up solutions
• Prescribing Morse scalar curvatures: critical points at infinity
• Prescribing scalar curvatures: non compactness versus critical points at infinity

Cited by in corpus (5)

• Prescribing Morse scalar curvatures: subcritical blowing-up solutions
• Prescribing Morse scalar curvatures: critical points at infinity
• On the ${\sigma }_k$-Nirenberg problem
• Prescribing Morse scalar curvatures: blow-up analysis
• Prescribing Morse scalar curvatures: incompatibility of non existence