Selected Papers of Oliver Schnürer

• Stetigkeitswürfel: Spielerisch den Umgang mit der Definition der Stetigkeit erlernen
  Ein Spiel zum intensiven und nichttrivialen Einüben der Stetigkeitsdefinition.
• Mean curvature flow without singularites
  We use one additional dimension and smooth graphical mean curvature flow. This gives a method to smoothly flow through singularities. We include several illustrations.
• Evolution of convex lens-shaped networks under curve shortening flow
  A paper written with 10 coauthors during a seminar.
• Self-similarly expanding networks to curve shortening flow
  Uses almost exclusively ordinary differential equations and elementary methods. It has been used in a student seminar.
• Entire spacelike hypersurfaces of constant Gauß curvature in Minkowski space
  We use Pogorelov type estimates to find smooth solutions of prescribed Gauß curvature. Before, we had solved such a problem based on global estimates, see Hypersurfaces of prescribed Gauß curvature in exterior domains.
• Stability of translating solutions to mean curvature flow
  In contrast to similar stability results for the Ricci flow, see below, the proof for mean curvature flow is based on barriers.
• Surfaces contracting with speed |A|²
  The main result of this paper uses the monotonicity of a function. We indicate how we used a computer to find this Lyapunov function. See Expandierende und kontrahierende Flächen for more examples of such monotone functions.
• Stability of gradient Kähler-Ricci solitons
  We use integral estimates to show that perturbations of the Kähler potential disappear eventually in a non-compact setting. In particular, the potential does not lift off, i. e. it does not converge to the original potential plus a constant. Integral estimates are also used in Stability of Euclidean space under Ricci flow to prove stability in a non-compact setting. For an example that a lift off can indeed happen see Decay at infinity for parabolic equations.
• Translating solutions for Gauß curvature flows with Neumann boundary condition
  The ice-cream cone estimate geometrically bounds the full gradient of a convex function when the normal derivative is bounded.
• Translating solutions to the second boundary value problem for curvature flows
  This includes a method to show convergence to a translating solution provided that there are appropriate a priori estimates.