A Riemannian definition of quasiregular mappings

Details A Riemannian definition of quasiregular mappings A Riemannian definition of quasiregular mappings

2011-10-04

arxiv.org/abs/1110.0639v1

Mathematics

Differential Geometry

16 pages

Scientific paper

In this paper, we give a new natural coordinate invariant definition of quasiconformal and quasiregular mappings on Riemannian manifolds. The new definition is given in terms of coordinate invariant trace and determinant. The definition can also be seen arising naturally from the inner product space structure the tangent spaces of Riemannian manifolds have. In case of Euclidean spaces, the definition is equivalent to the standard analytic definition of quasiregular mappings. We demon- strate how to use the new definition by finding an invariant conformal structure for quasiconformal groups on Riemannian manifolds.

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