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Daily Overview |
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DG4: Differential Geometry Location: A704 Session Chair: Oliver Schnürer Session Chair: Miles Simon | |
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On surfaces of constant spacetime mean curvature in Minkowski spacetime University of Tübingen, Germany Surfaces of constant spacetime (or co-dimension $2$) mean curvature (STCMC) have been shown to be abundant in the asymptotic end(s) of any asymptotically Minkowskian spacetime of non-vanishing mass (C.—Sakovich ’21). It has since been an open question how many STCMC-surfaces there are in Minkowski spacetime. We will explain why there are in fact many STCMC-surfaces in Minkowski spacetime. Our analysis is based on a characterization of local STCMC-foliations in relativistic initial data sets by Metzger—Pe\~nuela which in turn goes back to a local CMC-foliation result in Riemannian manifolds by Ye. We will also briefly touch on the corresponding Riemannian result by Yau who argues for rigidity of co-dimension $2$ constant mean curvature (CMC) surfaces in Euclidean $4$-space. In particular, we will indicate how the stark difference between the Euclidean and Minkowskian results can be resolved. | |
