Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Prescribing scalar curvatures: loss of minimizability (2406.10639v2)

Published 15 Jun 2024 in math.DG

Abstract: Prescribing conformally the scalar curvature on a closed manifold with negative Yamabe invariant as a given function $K$ is possible under smallness assumptions on $K_{+}=\max{K,0}$ and in particular, when $K<0$. In addition, while solutions are unique in case $K\leq 0$, non uniqueness generally holds, when $K$ is sign changing and $K_{+}$ sufficiently small and flat around its critical points. These solutions are found variationally as minimizers. Here we study, what happens, when the relevant arguments fail to apply, describing on one hand the loss of minimizability generally, while on the other we construct a function $K$, for which saddle point solutions to the conformally prescribed scalar curvature problem still exist.

Summary

We haven't generated a summary for this paper yet.