论文标题
Hyperkaehler 4-manifolds的紧凑定理
A compactness theorem for hyperkaehler 4-manifolds with boundary
论文作者
论文摘要
在本文中，我们研究了Hyperkaehler 4-manifolds的边界价值问题的紧凑性。我们表明，在某些拓扑条件和边界上的正平均曲率条件下，一系列Hyperkaehler三元序列在且仅当它们对边界的限制顺利地收敛到差异时，就会顺利收敛到差异。我们还将这一结果推广到无扭转的超愉快三连圆形三元。
In this paper, we study the compactness of a boundary value problem for hyperkaehler 4-manifolds. We show that under certain topological conditions and the positive mean curvature condition on the boundary, a sequence of hyperkaehler triples converges smoothly up to diffeomorphisms if and only if their restrictions to the boundary converge smoothly up to diffeomorphisms. We also generalize this result to torsion-free hypersymplectic triples.
