Corpus ID: 235458134

# Prescribing Morse scalar curvatures: incompatibility of non existence

@inproceedings{Mayer2021PrescribingMS,
title={Prescribing Morse scalar curvatures: incompatibility of non existence},
author={M. Mayer},
year={2021}
}
Given a closed manifold of positive Yamabe invariant and for instance positive Morse functions upon it, the conformally prescribed scalar curvature problem raises the question, whether or not such functions can by conformally changing the metric be realised as the scalar curvature of this manifold. As we shall quantify, the answer is depending on the complexity of these functions most likely yes and, if one such Morse function happens not to be conformally prescribable, most others can and this… Expand
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#### References

SHOWING 1-10 OF 44 REFERENCES
The scalar-curvature problem on the standard three-dimensional sphere
• Mathematics
• 1991
Let (S3, c) be the standard 3-sphere, i.e., the 3-sphere equipped with the standard metric. Let K be a C2 positive function on S3. The Kazdan-Warner problem [l] is the problem of finding suitableExpand
Prescribing Morse scalar curvatures: critical points at infinity
The problem of prescribing conformally the scalar curvature of a closed Riemannian manifold as a given Morse function reduces to solving an elliptic partial differential equation with criticalExpand
Non simple blow ups for the Nirenberg problem on half spheres
• Mathematics
• 2020
In this paper we study a Nirenberg type problem on standard half spheres (S+, g0) consisting of finding conformal metrics of prescribed scalar curvature and zero boundary mean curvature. This problemExpand
Prescribing Morse scalar curvatures: pinching and Morse theory
• Mathematics
• 2019
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 andExpand
Prescribing scalar curvatures: non compactness versus critical points at infinity
Abstract We illustrate an example of a generic, positive function K on a Riemannian manifold to be conformally prescribed as the scalar curvature, for which the corresponding Yamabe type L2-gradientExpand
Prescribing Morse scalar curvatures: Subcritical blowing-up solutions
• Mathematics
• 2018
Abstract Prescribing conformally the scalar curvature of a Riemannian manifold as a given function consists in solving an elliptic PDE involving the critical Sobolev exponent. One way of attackingExpand
Prescribing Morse scalar curvatures: blow-up analysis
• Mathematics
• 2018
We study finite-energy blow-ups for prescribed Morse scalar curvatures in both the subcritical and the critical regime. After general considerations on Palais-Smale sequences we determine preciseExpand
Large conformal metrics with prescribed scalar curvature
• Mathematics
• 2016
Let $(M,g)$ be a $n-$dimensional compact Riemannian manifold. Let $h$ be a smooth function on $M$ which has a local maximum point $\xi$ such that $h(\xi)=0.$ We are interested in finding conformalExpand
A scalar curvature flow in low dimensions
Let $$M^{n}$$Mn be a $$n=3,4,5$$n=3,4,5 dimensional, closed Riemannian manifold of positive Yamabe invariant. For a smooth function $$K>0$$K>0 on M we consider a conformal flow, that tends toExpand
Conformal transformation of metrics on the n-sphere
• Mathematics
• 2013
Abstract The purpose of this work is to discuss some new results on the scalar curvature problem in dimension n ≥ 3 . We give precise estimates on the losses of compactness and we prove the existenceExpand