Smoczyk J N
Research in Toronto

Geometric evolution equations have been applied to a variety of problems in differential geometry, topology, analysis and physics. Mean curvature flows in higher codimension and Lagrangian mean curvature flows are of particular interest. Applications include the Penrose inequality, integrable almost complex structures, Yang-Mills and Einstein connections, almost complex structures and metrics such as minimal and harmonic maps, connections, existence of canonical maps, Arnol'd conjecture, the Schönfliess conjecture, the 1/4-pinching theorem, classification of Riemannian and Kählerian manifolds, uniformization theorems in Kähler geometry, Poincaré and geometrization conjectures, Einstein metrics and metrics of prescribed scalar or Ricci curvature.The research interests of Professor Knut Smoczyk and his group mainly focus on geometric evolution equations. Lagrangian mean curvature flows exist on Kähler-Einstein manifolds and more generally on almost Kähler manifolds equipped with an Einst.