论文标题
标量曲率的边界条件
Boundary conditions for scalar curvature
论文作者
论文摘要
基于Atiyah-Patodi-Singer指数公式，我们构建了无限K-Area自旋歧管上平均凸边界的正标度曲率指标的阻塞。我们还表征了极端情况。接下来，我们显示了具有较低标量曲率边界的指标的边界条件的一般变形原理。这意味着边界条件的放松通常会引起此类指标空间的弱同质词。这可以用来完善复合sIndularIte a miao的平滑和边界条件的变形，la brendle-marques-neves等。最后，我们构建了紧凑的歧管，为此，具有平均凸边界的正标曲率指标的空间具有非平凡的较高同型基团。
Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite K-area. We also characterize the extremal case. Next we show a general deformation principle for boundary conditions of metrics with lower scalar curvature bounds. This implies that the relaxation of boundary conditions often induces weak homotopy equivalences of spaces of such metrics. This can be used to refine the smoothing of codimension-one singularites a la Miao and the deformation of boundary conditions a la Brendle-Marques-Neves, among others. Finally, we construct compact manifolds for which the spaces of positive scalar curvature metrics with mean convex boundaries have nontrivial higher homotopy groups.
