题 目：The total squared curvature functional forsurfaces in manifolds
报告人：Ernst Kuwert (Freiburg Univ., German)
摘 要： We review joint work with A. Mondino and J. Schygulla on the existence of immersed $2$-spheres minimizing the total squared curvature in a compact Riemannian $3$-manifold $M$. In that paper, we assumed that $M$ has strictly positive sectional curvature to bound the area of the minimizing sequence. In the second part of the talk, we present a recent result with V. Bangert. For a sequence of compact immersed surfaces with bounded total squared curvature in a compact Riemannian $n$-manifold, the area is automatically bounded along the sequence unless there is a complete, totally geodesic immersion into $M$. It is known that the second alternative is not generic.
时 间:2018年5月30日 14:00—16:00