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日時: 2015年9月25日(金) 16:50〜17:50
会場: 数理科学研究科棟(駒場) 大講義室
Gerhard Huisken (The Mathematisches Forschungsinstitut Oberwolfach)
Mean curvature flow with surgery
We study the motion of hypersurfaces in a Riemannian manifold with normal velocity equal to the mean curvature of the evolving hypersurface. In general this quasilinear, parabolic evolution system may have complicated singularities in finite time. However, under natural assumptions such as embeddedness of the surface and positivity of the mean curvature (case of 2-dimensional surfaces) all singularities can be classified and developing "necks" can be removed by a surgery procedure similar to techniques employed by Hamilton and Perelman in the Ricci-flow of Riemannian metrics. The lecture describes results and techniques for mean curvature flow with surgery developed in joint work with C. Sinestrari and S. Brendle.
http://www.mfo.de/about-the-institute/staff/prof.-dr.-gerhard-huisken