规定Morse标量曲率：不存在性的不相容性
Prescribing Morse scalar curvatures: incompatibility of non existence
AI总结：
研究在正Yamabe不变量闭 manifold 上，通过 conformal 变换是否能将给定的Morse函数作为标量曲率的问题，揭示不存在性与能量有界解之间的关系。
摘要：
给定一个具有正Yamabe不变量的闭 manifold，以及在其上的正Morse函数， conformally prescribed scalar curvature 问题提出疑问：是否可以通过 conformal 变换度量使这些函数成为该 manifold 的标量曲率。我们将根据这些函数的形状和结构量化地证明，对于某些候选函数不存在解会导致整个相关候选函数类中存在能量有界解。
英文摘要：
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.
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