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The integrability of a field of endomorphisms

Gerard Thompson (2002)

Mathematica Bohemica

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 p -harmonic functions

Roger Moser (2007)

Journal of the European Mathematical Society

We consider the level set formulation of the inverse mean curvature flow. We establish a connection to the problem of p -harmonic functions and give a new proof for the existence of weak solutions.

The Killing Tensors on an n -dimensional Manifold with S L ( n , ) -structure

Sergey E. Stepanov, Irina I. Tsyganok, Marina B. Khripunova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an n -dimensional differentiable manifold M endowed with an equiaffine S L ( n , ) -structure and discuss possible applications of obtained results in Riemannian geometry.

The Nash-Kuiper process for curves

Vincent Borrelli, Saïd Jabrane, Francis Lazarus, Boris Thibert (2011/2012)

Séminaire de théorie spectrale et géométrie

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 ( J r T * ) *

Włodzimierz M. Mikulski (2000)

Archivum Mathematicum

For natural numbers r and n 2 a complete classification of natural affinors on the natural bundle ( J r T * ) * dual to r -jet prolongation J r T * of the cotangent bundle over n -manifolds is given.

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