Positive mass theorems of ALF and ALG manifolds
Positive mass theorems of ALF and ALG manifolds
*Please note the change in time*
Zoom link:Ìý
In this talk, we will discuss positive mass theorems for ALF and ALG manifolds with Ìýdimensions no greater than 7. Different from theÌýcompatibility condition for spin structure in Theorem 2 of V. Minerbe’s paperÌýA mass for ALF manifolds, Comm. Math. Phys. 289 (2009), no. 3, 925–955, weÌýshow that some type of simple topological conditions of manifolds is enough to guarantee the nonnegativity of the mass. As in the asymptotically flatÌýcase, we reduce the desired positive mass theorems to those ones concerning non-existence of positive scalar curvature metrics on closed manifoldsÌýcoming from generalize surgery toÌý$n$-torus. Finally, we investigate certain fill-in problems and obtain an optimal bound for total meanÌýcurvature of admissible fill-ins for flat product 2-torus.Ìý
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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: