Ernst Kuwert

Evolution of Elastic Curves in

We consider curves in

\Rn

{\mathbb R}^n

: Existence and Computation

moving by the gradient flow for elastic energy, i.e., the L2 integral of curvature. Long-time existence is proved in the two cases when a multiple of length is added to the energy or the length is fixed as a constraint. Along these lines, a lower bound for the lifespan of solutions to the curve diffusion flow is observed. We derive algorithms for both the elastic flows and the curve diffusion equation. After a numerical test we compute several examples, including cases of curve diffusion in which a singularity develops.

Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds

We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold

Note on the Isoperimetric Profile of a Convex Body

M

Area-minimizing disks with free boundary and prescribed enclosed volume

M. Under the assumption that the sectional curvature

Embedded solutions for exterior minimal surface problems

K^M