穿孔四流形上的自旋与数量曲率
Spin and scalar curvature on punctured four manifolds
- University of Maryland（马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明非零符号差的闭自旋四流形在穿孔后仍不允许一致正数量曲率的完备度量，并发现Gromov的μ-气泡可作为APS边界问题的便捷边界。
AI中文摘要：
我们证明，一个具有非零符号差的闭自旋四流形，即使在被打孔后，也不允许具有一致正数量曲率的完备度量。特别地，穿孔的$K3$曲面不允许这样的度量。已知在更高维度中这一结论不成立。一个关键的新观察，可能具有独立意义，是Gromov的$\u03bc$-气泡是Dirac算子的APS边界值问题的一类方便的边界。
英文摘要：
We show that a closed spin four-manifold with nonzero signature, even after being punctured, does not admit a complete metric with uniformly positive scalar curvature. In particular, the punctured $K3$ surface does not admit such a metric. This is known to be false in higher dimensions. A key new observation, which could be of independent interest, is that Gromov's $μ$-bubbles are a convenient class of boundaries for the APS boundary value problem for the Dirac operator.
