The characterization of the spherical timelike curves in 3-dimensional Lorentzian space.
The Clairaut's theorem on rotational surfaces in pseudo-Euclidean 4-space with index 2
Clairaut’s theorem is expressed on the surfaces of rotation in semi Euclidean 4-space. Moreover, the general equations of time-like geodesic curves are characterized according to the results of Clairaut's theorem on the hyperbolic surfaces of rotation and the elliptic surface of rotation, respectively.
The classification of 3-dimensional locally strongly convex homogeneous affine hypersurfaces.
The Classification of Hypersurfaces of a Euclidean Space with Parallel Higher Order Fundamental Form.
The conjugacy problem for relatively hyperbolic groups.
The convex and concave decomposition of manifolds with real projective structures
The convex floating body.
The CUDA implementation of the method of lines for the curvature dependent flows
We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs - the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge-Kutta-Merson solver. It is a robust solver with an automatic choice of the...
The Curvature of Most Convex Surfaces Vanishes Almost Everywhwere.
The curvatures of certain surfaces of translation
The Cusp Catastrophe of Thom in the Bifurcation of Minimal Surfaces.
The cyclides of third order in pseudoisotropic space. II. (Die Zykliden 3. Ordnung im pseudoisotropen Raum. II.)
The Darboux mapping of canal hypersurfaces.
The Darboux theorem on plane trajectories of two-parametric space motions
The paper contains the proof of the classification theorem for two-parametric space motions with at least 5 points with plane trajectories. The proof is based on [1] and on the cannonical form of a certain tensor of order 3. The second part of the paper deals with the problem of plane trajectories from the differential-geometrical point of view. Some applications are given.
The development of the oloid.
The differential properties of one class of surfaces in Euclidean space.
The Dirichlet problem for the equation of prescribed mean curvature
The double bubble conjecture.
The double bubble problem in spherical and hyperbolic space.
The double bubble problem on the cone.