Calculus of Variations and Geometric Measure Theory
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A. Malchiodi - M. Mayer

Prescribing Morse scalar curvatures: pinching and Morse theory

created by malchiodi on 07 Sep 2019

[BibTeX]

Preprint

Inserted: 7 sep 2019
Last Updated: 7 sep 2019

Pages: 32
Year: 2019

Abstract:

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.


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