Branching solutions to one-dimensional variational problems (Q2718903)

This is a monograph which studies Steiner trees. The Steiner minimum tree is a shortest network interconnecting a finite set of points in a metric space. In this book, it is also considered as a branching solution of a one-dimensional variational problem. Starting with this consideration, the authors have done a sequence of research works which builds a bridge between discrete mathematics and differential geometry. Indeed, the Steiner tree has been put into manifolds in this book. Meanwhile, there are many open problems proposed by this book.NEWLINENEWLINENEWLINEThe book consists of six chapters. The first chapter contains preliminary results. The second chapter is about network extremality criteria. The third chapter is on linear networks in \(\mathbb{R}^n\). From chapter four to six, one-dimensional variational problems with different functionals are solved and as their branching solutions several Steiner trees in general forms are presented. Finally, sixty-two open problems are mentioned in the appendix. In summary, this is a nice contribution to the study of Steiner trees and a useful reference to the researchers in mathematics and computer science.