We consider the problem of prescribing conformally the scalar curvature on compact manifolds of positive Yamabe class in dimension n ≥ 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.

Prescribing Morse scalar curvatures: pinching and Morse theory

Malchiodi, Andrea
;
Mayer, Martin
2023

Abstract

We consider the problem of prescribing conformally the scalar curvature on compact manifolds of positive Yamabe class in dimension n ≥ 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.
2023
Settore MAT/05 - Analisi Matematica
Conformal geometry, Morse theory, Min-max theory, blow-up analysis.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/81853
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