Positive mass theorems of ALF and ALG manifolds

  地点：工商楼200-9会议室

  摘要: 

  In this talk, we will prove positive mass theorems for ALF and ALG manifolds with model spaces $R^{n-1}\times S^1$ and $R^{n-2}\times T^2$ respectively in dimensions no greater than 7. Different from the compatibility condition for spin structure in Theorem 2 of V. Minerbe’s paper A mass for ALF manifolds, Comm. Math. Phys. 289 (2009), no. 3, 925–955 we show that some type of incompressible condition for $S^1$ and $T^2$ is enough to guarantee the nonnegativity of the mass. As in the asymptotically flat case, we reduce the desired positive mass theorems to those ones concerning non-existence of positive scalar curvature metrics on closed manifolds coming from generalize surgery to -torus. Finally, we investigate certain fill-in problems and obtain an optimal bound for total mean curvature of admissible fill-ins for flat product 2-torus $S^1(l_1)\times S^1(l_2)$. This talk is based on the paper joint with my Ph.D. students Peng Liu and Jintian Zhu, here is the link of the paper :http://arxiv.org/abs/2103.11289.