Math @ Duke

Publications [#354054] of Demetre P Kazaras
Papers Published
 Botvinnik, Boris; Kazaras, Demetre, Minimal hypersurfaces and bordism of positive scalar curvature metrics,
Math. Ann., vol. 371 no. 12
(2018),
pp. 189224
(last updated on 2020/12/18)
Abstract: Let (Y, g) be a compact Riemannian manifold of positive scalar curvature (psc). It is wellknown, due to Schoenâ€“Yau, that any closed stable minimal hypersurface of Y also admits a pscmetric. We establish an analogous result for stable minimal hypersurfaces with free boundary. Furthermore, we combine this result with tools from geometric measure theory and conformal geometry to study pscbordism. For instance, assume (Y_0,g_0) and (Y_1,g_1) are closed pscmanifolds equipped with stable minimal hypersurfaces X_0 \subset Y_0 and X_1\subset Y_1. Under natural topological conditions, we show that a pscbordism (Z,{\bar{g}}) : (Y_0,g_0)\rightsquigarrow (Y_1,g_1) gives rise to a pscbordism between X_0 and X_1 equipped with the pscmetrics given by the Schoenâ€“Yau construction.


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