We consider the problem of prescribing conformally the scalar curvature on compact manifolds of positive Yamabe class in dimension (Formula presented.). 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 nonexistence results showing the sharpness of some of our assumptions, both in terms of the dimension and of the Morse structure of the prescribed function. © 2021 Wiley Periodicals, Inc.

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 (Formula presented.). 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 nonexistence results showing the sharpness of some of our assumptions, both in terms of the dimension and of the Morse structure of the prescribed function. © 2021 Wiley Periodicals, Inc.
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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