Publications [#354054] of Demetre P Kazaras

Papers Published

1. Botvinnik, Boris; Kazaras, Demetre, Minimal hypersurfaces and bordism of positive scalar curvature metrics, Math. Ann., vol. 371 no. 1-2 (2018), pp. 189-224
   (last updated on 2020/12/18)

   Abstract:
   Let (Y, g) be a compact Riemannian manifold of positive scalar curvature (psc). It is well-known, due to Schoen–Yau, that any closed stable minimal hypersurface of Y also admits a psc-metric. 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 psc-bordism. For instance, assume (Y_0,g_0) and (Y_1,g_1) are closed psc-manifolds equipped with stable minimal hypersurfaces X_0 \subset Y_0 and X_1\subset Y_1. Under natural topological conditions, we show that a psc-bordism (Z,{\bar{g}}) : (Y_0,g_0)\rightsquigarrow (Y_1,g_1) gives rise to a psc-bordism between X_0 and X_1 equipped with the psc-metrics given by the Schoen–Yau construction.