Harmonic Maps between Riemannian Polyhedra [Hardcover]

A research level book on harmonic maps between singular spaces, by renowned authors, first published in 2001.This is a research-level monograph on harmonic maps between singular spaces. The theory of harmonic maps between spaces without singularities has many important applications throughout mathematics. In this book, the authors set out much new material on harmonic maps between singular spaces for the first time in one place, considering in particular the case of Riemannian polyhedra, the properties of which are especially suitable for this. The work will serve as a concise source and reference for all researchers working in this field or a similar one.This is a research-level monograph on harmonic maps between singular spaces. The theory of harmonic maps between spaces without singularities has many important applications throughout mathematics. In this book, the authors set out much new material on harmonic maps between singular spaces for the first time in one place, considering in particular the case of Riemannian polyhedra, the properties of which are especially suitable for this. The work will serve as a concise source and reference for all researchers working in this field or a similar one.This research-level monograph on harmonic maps between singular spaces sets out much new material on the theory, bringing all the research together for the first time in one place. Riemannian polyhedra are a class of such spaces that are especially suitable to serve as the domain of definition for harmonic maps. Their properties are considered in detail, with many examples being given, and potential theory on Riemmanian polyhedra is also considered. The work will serve as a concise source and reference for all researchers working in this field or a similar one.Gromov's preface; Preface; 1. Introduction; Part I. Domains, Targets, Examples: 2. Harmonic spaces, Dirichlet spaces and geodesic spaces; 3. Examples of domains and targets; 4. Riemannian polyhedra; Part II. Potel…