Harmonic maps between Riemannian polyhedra. With a preface by M. Gromov (Q2732563)

Given two spaces \(X\) and \(Y\), suppose a harmonic structure on \(X\), that is, a distinguished space of real-valued functions on \(X\) regarded as ``harmonic''. Further, one may define another space of ``subharmonic functions'' on \(X\). In parallel, the functions on \(Y\) are distinguished as ``convex functions''. A map \(f:X\to Y\) is called ``harmonic'' if the pull-back of every ``convex function'' on \(Y\) is ``subharmonic'' on \(X\).NEWLINENEWLINENEWLINEThe authors specialize the ``measurable Riemannian'' structures of polyhedra for both \(X\) and \(Y\). The book contains an introduction and three parts: (I) Domains, targets and examples; (II) Potential theory on polyhedra; (III) Maps between polyhedra.