Calculus of Variations and Geometric Measure Theory

M. Mayer

Prescribing Morse scalar curvatures: incompatibility of non existence

created by mayer1 on 14 Apr 2023

[BibTeX]

preprint

Inserted: 14 apr 2023

Year: 2021

ArXiv: 2106.09294 PDF

Abstract:

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 depending on the shape and structure of such functions, every lack of a solution for some candidate function leads to existence of energetically uniformly bounded solutions for entire classes of related candidate functions.