The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
We study the evolution of a closed, convex hypersurface in in direction of its normal vector, where the speed equals a power of the mean curvature. We show that if initially the ratio of the biggest and smallest principal curvatures at every point is close enough to , depending only on and , then this is maintained under the flow. As a consequence we obtain that, when rescaling appropriately as the flow contracts to a point, the evolving surfaces converge to the unit sphere.
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 curves that all start at one point, where they form degree angles, and expands homothetically under curve shortening flow. We also prove uniqueness of these networks.
Download Results (CSV)