In this lecture, we aim to present some rigidity results for compact initial data sets, in both the boundary and no boundary cases.
For example, under natural energy, boundary, and topological conditions, we obtain a global version of a well-known result of H. Bray, S. Brendle, and A. Neves. We also prove some extensions of results obtained, in a previous work, by M. Eichmair, G.J. Galloway, and the author. Finally, as time permits, we are going to present a number of examples in order to illustrate some of the results presented in this lecture.
This is part of a joint work with G.J. Galloway.
Abraao Mendes (Brasil): Some rigidity results for compact initial data sets
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