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 precise blow up rates for subcritical solutions: in particular the possibility of tower bubbles is excluded in all dimensions. In subsequent papers we aim to establish the sharpness of this result, proving a converse existence statement, together with a one to one correspondence of blowing-up subcritical solutions and {\em critical points at infinity}. This analysis will be then applied to deduce new existence results for the geometric problem.

中文翻译：

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规定莫尔斯标量曲率：爆炸分析

我们研究了亚临界和临界状态下规定的莫尔斯标量曲率的有限能量爆炸。在对 Palais-Smale 序列进行一般考虑之后，我们确定了亚临界解决方案的精确膨胀率：特别是在所有维度中都排除了塔气泡的可能性。在随后的论文中，我们的目标是建立这个结果的锐度，证明一个相反的存在陈述，以及爆炸亚临界解和 {\em 临界点在无穷远} 的一一对应关系。然后将应用该分析来推导出几何问题的新存在结果。