Expandierende und kontrahierende Flächen

We show that strictly convex surfaces contracting with normal velocity equal to |A|² shrink to a point in finite time. After appropriate rescaling, they converge to spheres.

Strictly convex surfaces that expand by the inverse Gauß curvature flow converge to infinity in finite time. After appropriate rescaling, they converge to spheres.

We describe the algorithm to find our main test functions.

See also:

• Surfaces Expanding by the Inverse Gauß Curvature Flow,
  J. reine angew. Math. 600 (2006), 117-134.
• Surfaces Contracting with Speed |A|²,
  J. Differential Geom. 71 (2005), no. 3, 347-363.