关于Q-曲率正性的连续性方法注记
A note on the positivity of $Q$-curvature via the continuity method
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中文总结 AI 辅助
针对满足特定Yamabe不变量条件的5维闭黎曼流形，借助连续性方法证明其共形类中存在兼具正标量曲率与正Q-曲率的度量。
中文摘要 AI 辅助
设(M,g)为光滑闭5维黎曼流形，满足Yamabe不变量Y(M,[g])>0、Yamabe型Q-曲率不变量Y₄^*(M,[g])>0。借助连续性方法，在共形类[g]中存在满足正标量曲率与正Q-曲率的度量，前提是共形类[g]中存在满足附加条件的“初始度量”。
英文摘要
Suppose $(M, g)$ is a smooth, closed, $5$-dimensional Riemannian manifold with positive Yamabe invariant $Y(M, [g]) > 0$ and positive Yamabe-type $Q$-curvature invariant $Y_{4}^{\ast}(M, [g]) > 0$. Using the continuity method, we prove the existence of a metric in the conformal class $[g]$ with positive scalar curvature and positive $Q$-curvature, assuming an additional condition on an ``initial metric" in the class $[g]$.
