MCF in 2D:
κ = curvature at each point.
Points move inward at rate κ.
Gage-Hamilton-Grayson (1987):
Any smooth embedded closed curve flows to a round point.
Dumbbell: neck pinches in finite time — topology change!
Perimeter: —
Area: —
Isoperimetric: —
4πA/L² → 1 as → circle
κ = curvature at each point.
Points move inward at rate κ.
Gage-Hamilton-Grayson (1987):
Any smooth embedded closed curve flows to a round point.
Dumbbell: neck pinches in finite time — topology change!
Perimeter: —
Area: —
Isoperimetric: —
4πA/L² → 1 as → circle