# Positive mass theorems of ALF and ALG manifolds

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Yuguang Shi, Peking University

*Please note the change in time*

Zoom linkhttps://princeton.zoom.us/j/594605776

In this talk, we will discuss positive mass theorems for ALF and ALG manifolds with  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 simple topological conditions of manifolds 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 $n$-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.

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