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Colloquium
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Organizer(s) | ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair) |
|---|---|
| URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index_e.html |
2015/09/25
16:50-17:50 Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Gerhard Huisken (The Mathematisches Forschungsinstitut Oberwolfach )
Mean curvature flow with surgery
http://www.mfo.de/about-the-institute/staff/prof.-dr.-gerhard-huisken
Gerhard Huisken (The Mathematisches Forschungsinstitut Oberwolfach )
Mean curvature flow with surgery
[ Abstract ]
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.
[ Reference URL ]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
