Stability of mean convex cones under mean curvature flow (2008)
Clutterbuck, Julie, Schnürer, Oliver C.
We consider graphical solutions to mean curvature flow and obtain a stability result for homothetically expanding solutions coming out of cones of positive mean curvature: If another solution is...
Evolution of convex lens-shaped networks under curve shortening flow (2007)
Schnürer, Oliver C., Azouani, Abderrahim, Georgi, Marc, Hell, Juliette, Jangle, Nihar, Koeller, Amos, ...
We consider convex symmetric lens-shaped networks in R^2 that evolve under curve shortening flow. We show that the enclosed convex domain shrinks to a point in finite time. Furthermore, after...
Stability of Euclidean space under Ricci flow (2007)
Schnürer, Oliver C., Schulze, Felix, Simon, Miles
We study the Ricci flow for initial metrics which are C^0 small perturbations of the Euclidean metric on R^n. In the case that this metric is asymptotically Euclidean, we show that a Ricci harmonic...
Self-similarly expanding networks to curve shortening flow (2007)
Schnürer, Oliver C., Schulze, Felix
We consider a network in the Euclidean plane that consists of three distinct half-lines with common start points. From that network as initial condition, there exists a network that consists of three...
Entire spacelike hypersurfaces of constant Gauss curvature in Minkowski space (2006)
Bayard, Pierre, Schnürer, Oliver C.
We prove existence and stability of smooth entire strictly convex spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space. The proof is based on barrier constructions and local a...
Stability of translating solutions to mean curvature flow (2005)
Clutterbuck, Julie, Schnürer, Oliver C., Schulze, Felix
We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large...
Decay at infinity for parabolic equations (2005)
Schnürer, Oliver C., Schwetlick, Hartmut R.
We consider solutions to linear parabolic equations with initial data decaying at spatial infinity. For a class of advection-diffusion equations with a spatially dependent velocity field, we study...
Convex functions with unbounded gradient (2005)
We show that domains, that allow for convex functions with unbounded gradient at their boundary, are convex.
Surfaces expanding by the inverse Gauss curvature flow (2004)
We show that strictly convex surfaces expanding by the inverse Gauss curvature flow converge to infinity in finite time. After appropriate rescaling, they converge to spheres. We describe the...
Surfaces contracting with speed |A|^2 (2004)
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. We indicate how we used...