We consider the problem of prescribing conformally the scalar curvature on compact manifolds of positive Yamabe class in dimension . 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 nonexistence results showing the sharpness of some of our assumptions, both in terms of the dimension and of the Morse structure of the prescribed function. © 2021 Wiley Periodicals, Inc.

中文翻译：

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规定莫尔斯标量曲率：收缩和莫尔斯理论

我们考虑在维数为 的正 Yamabe 类紧流形上保形地规定标量曲率的问题。我们使用莫尔斯理论证明了新的存在性结果，并对曲率函数在合适的收缩条件下的爆破解进行了一些分析。我们还提供了新的不存在结果，显示了我们的一些假设的清晰度，无论是在规定函数的维数还是莫尔斯结构方面。© 2021 Wiley Periodicals, Inc. 版权所有。