Ali Aleyasin, Université du Québec à Montréal
"The Calabi problem on edge-cone manifolds"
Let M be a Kähler manifold and V a complex hypersurface in it. A Kähler edge-cone metric along V is one with conical singularity along a complex hypersurface, that is, a metric which asymptotically resembles a cone metric on $\mathbb{R}^2$ in the directions normal to the hypersurface, and is smooth in the tangential directions. The study of problems around such singularities has received attention thanks to their role in understanding the relation between K-stability and the existence of Kähler-Einstein metrics on Fano manifolds. In this talk, we shall present some observations which help us derive new a priori estimates for the Calabi problem on such manifolds, still using classical methods. Further, we show new regularity results for canonical metrics of edge-cone type.
MC 5413