The homogeneous parallel- movement-mechanism. (Der homogene Paralleltrieb-Mechanismus.)
The Hurwitz Relation for Tori.
The hyperbolic n-space as a graph in euclidean (6n-6)-space.
The integrability of a field of endomorphisms
A Theorem is proved that gives intrinsic necessary and sufficient conditions for the integrability of a zero-deformable field of endomorphisms. The Theorem is proved by reducing to a special case in which the endomorphism field is nilpotent. Many arguments used in the derivation of similar results are simplified, principally by means of using quotient rather than subspace constructions.
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 isoperimetric inequality and the total absolute curvature of closed curves in spheres.
The isoperimetric inequality for a minimal surface with radially connected boundary
The Killing Tensors on an -dimensional Manifold with -structure
In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an -dimensional differentiable manifold endowed with an equiaffine -structure and discuss possible applications of obtained results in Riemannian geometry.
The Logarithmic Hardy-Littlewood-Sobolev Inequlity and Extremals of Zeta Functions on Sn.
The Martin compactification of the Cartesian product of two hyperbolic spaces.
The maximum principle at infinity for minimal surfaces in flat three manifolds.
The mean curvature of the second fundamental form of a hypersurface.
The Moduli Space of Complete Embedded Constant Mean Cuvature Surfaces.
The Monge-Ampère equation and affine maximal surfaces.
The Nash-Kuiper process for curves
A strictly short embedding is an embedding of a Riemannian manifold into an Euclidean space that strictly shortens distances. From such an embedding, the Nash-Kuiper process builds a sequence of maps converging toward an isometric embedding. In that paper, we describe this Nash-Kuiper process in the case of curves. We state an explicit formula for the limit normal map and perform its Fourier series expansion. We then adress the question of Holder regularity of the limit map.
The natural affinors on
For natural numbers and a complete classification of natural affinors on the natural bundle dual to -jet prolongation of the cotangent bundle over -manifolds is given.
The natural affinors on
The natural functions on the cotangent bundle of higher order vector tangent bundles over fibered manifolds
For natural numbers r,s,q,m,n with s≥r≤q we determine all natural functions g: T *(J (r,s,q)(Y, R 1,1)0)*→R for any fibered manifold Y with m-dimensional base and n-dimensional fibers. For natural numbers r,s,m,n with s≥r we determine all natural functions g: T *(J (r,s)(Y, R)0)*→R for any Y as above.
The natural operators lifting vector fields to generalized higher order tangent bundles
For natural numbers and and a real number we construct a natural vector bundle over -manifolds such that is the (classical) vector tangent bundle of order . For integers and and a real number we classify all natural operators lifting vector fields from -manifolds to .
The natural operators lifting vector fields to
For integers and a complete classification of all natural operators lifting vector fields to vector fields on the natural bundle dual to -jet prolongation of the cotangent bundle over -manifolds is given.