Mean Curvature Flow

§ 1 Mean curvature flow   [Introduction]      [Soliton of MCF簡介]   [面積變分法與MCF]  [MCF與Ricci flow中的neckpinch(頸部收縮)比較]

  1. Curve shortening flow  [CSF]
  2. Maximal principle
  3. Shrinkers
  4. The shrinker equation
  5. Huisken theorem

§ 2 Singularities for MCF

  1. Huisken monotonicity
  2. Tangent flows
  3. Mean convex flows
  4. Gaussian integral and F-functionals
  5. critical points for the F-functional
  6. F-stable or index 0 critical points

§ 3 generic(一般的) singularities

  1. How entropy is used
  2. Classification of entropy stable singularities
  3. Self-shrinkers with low entropy/Gaussian surface area

§ 4 Rigidity of cylinders

4.1 asymptotic rigidity

§5 Uniqueness of tangent flow

  1. Lojasiewicz innequalities
  2. Lojasiewicz innequalities for noncompact hypersurfaces and MCF

§ 6 The singular set of MCF with generic singularities

§ 7 Isolated singularirits

§ 8 Two conjectures about singularities of MCF

  1. Negative gradient flow near a critical point
  2. Flows beginning at a typical hypersurface avoid unstable singularities

§ 9 Dynamics of closed singularities

  1. Dynamics near a closed shrinker
  2. The heuristics(啟發式) of the local dynamics

§ Surgery in low dimensions

§ The surgery exact sequence for a disk

§ Dimension 4

§ Bounded surgery