Tautness and Lie Sphere Geometry.
Tensor product surfaces in and Lie groups.
Tensor product surfaces of a Euclidean space curve and a Euclidean plane curve.
The boundary value Minkowski problem. The parametric case
The Classification of Hypersurfaces of a Euclidean Space with Parallel Higher Order Fundamental Form.
The duals of generic hypersurfaces.
The faces of the Grassmanian of three-planes in R7 (Calibrated geometries on R7).
The Gauss Map for Surfaces in 4-Space.
The hyperbolic n-space as a graph in euclidean (6n-6)-space.
The inverse mean curvature flow and -harmonic functions
We consider the level set formulation of the inverse mean curvature flow. We establish a connection to the problem of -harmonic functions and give a new proof for the existence of weak solutions.
The volume conjecture and four-dimensional hypersurfaces
The volume preserving mean curvature flow.
Theory of semisymmetric conformally flat and biharmonic submanifolds.
Total curvature for knotted surfaces.
Transformations between surfaces in with flat normal and/or tangent bundles.
Transformations for hypersurfaces with vanishing Gauss-Kronecker curvature.
Transnormal graph surfaces.
Transnormal graphs
Transnormal partial tubes.
Two-dimensional curvature functionals with superquadratic growth
For two-dimensional, immersed closed surfaces , we study the curvature functionals and with integrands and , respectively. Here is the second fundamental form, is the mean curvature and we assume . Our main result asserts that critical points are smooth in both cases. We also prove a compactness theorem for -bounded sequences. In the case of this is just Langer’s theorem [16], while for we have to impose a bound for the Willmore energy strictly below as an additional condition....