An existence result of energy minimizer maps between riemannian polyhedra

Details An existence result of energy minimizer maps between riemannian polyhedra An existence result of energy minimizer maps between riemannian polyhedra

2004-08-18

arxiv.org/abs/math/0408248v4

Mathematics

Differential Geometry

15 pages

Scientific paper

In this paper, we prove the existence of energy minimizers in each free
homotopy class of maps between polyhedra with target space without focal
points. Our proof involves a careful study of some geometric properties of
riemannian polhyedra without focal points. Among other things, we show that on
the relevant polyhedra, there exists a convex supporting function.

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