标题： CMC巴特尼克数据的渐近平坦扩展 显示英文标题

标题： Asymptotically flat extensions of CMC Bartnik data

摘要： 设 $g$ 是 $2$-球面 $\mathbb{S}^2$上的度量，具有正高斯曲率，且 $H$ 是一个正常数。 在对$(g, H)$的适当条件下，我们构造了光滑的、渐近平坦的$3$-流形$M$，其标量曲率为非负，外极小边界与$(\mathbb{S}^2, g)$等距，并具有平均曲率$H$，使得在无穷远处$M$与一个空间 Schwarzschild 流形等距，其质量$m$可以被做得与$(\mathbb{S}^2,g,H)$的 Hawking 质量的常数倍任意接近。 此外，这个常数乘性因子仅依赖于$(g, H)$并且当$H$趋向于$0$时趋向于$1$。 该结果提供了与这种边界数据相关的巴特尼克质量的新上界。 显示英文摘要

摘要： Let $g$ be a metric on the $2$-sphere $\mathbb{S}^2$ with positive Gaussian curvature and $H$ be a positive constant. Under suitable conditions on $(g, H)$, we construct smooth, asymptotically flat $3$-manifolds $M$ with non-negative scalar curvature, with outer-minimizing boundary isometric to $(\mathbb{S}^2, g)$ and having mean curvature $H$, such that near infinity $M$ is isometric to a spatial Schwarzschild manifold whose mass $m$ can be made arbitrarily close to a constant multiple of the Hawking mass of $(\mathbb{S}^2,g,H)$. Moreover, this constant multiplicative factor depends only on $(g, H)$ and tends to $1$ as $H$ tends to $0$. The result provides a new upper bound of the Bartnik mass associated to such boundary data.