AbstractLagrangian mean curvature flow (LMCF) is a canonical way to deform Lagrangian submanifoldsin CalabiYau manifolds, with the goal of finding special Lagrangians, which are volume-minimizerswithin their homology classes. Despite its significance, the general long-time behavior of LMCFremains open. In this talk, l will present recent joint work with Chung-Jun Tsai and Albert Woodwhere we co...
AbstractThe scalar curvature of a Riemannian metric is interesting not only in analysis, geometry, and topology, but also in physics. Enlargeable Length-structures will be introduced and showed that it is a new obstruction to the existence of a Riemannian metric with positive scalar curvature (PSC-metric). Thus, the connected sum of a closed manifold with some of locally CAT(0)-manifolds carry ...