Aleksandrov-Rassias Problems on Distance Preserving Mappings

This book provides readers with an engaging explanation of the Aleksandrov problem, giving readers an overview of the process of solving Aleksandrov-Rassias problems, which are still actively studied by many mathematicians, and familiarizing readers with the details of the proof process. In addition, effort has been put into writing this book so that readers can easily understand the content, saving readers the trouble of having to search the literature on their own. In fact, this book logically and kindly introduces the basic theories of related fields.

Preface.- Preliminaries.- Aleksandrov Problem.- Aleksandrov-Benz Problem.-  Aleksandrov-Rassias Problems.- Rassias and Xiang’s Partial Solutions.- Inequalities for Distances between Points.- Jung, Lee, and Nam’s Partial Solutions.- Miscellaneous.- Bibliography.- Index.

Soon-Mo Jung was a mathematics professor at Hongik University in Republic of Korea from March 1995 to February 2023. His research interests include measure theory, number theory, Euclidean geometry, and classical analysis. He received his bachelor's, master's and doctoral degrees in 1988, 1992 and 1994, respectively, from the Department of Mathematics at the University of Stuttgart, Germany. In particular, among his important research topics, classical analysis and Euclidean geometry account for a large portion, and these topics are closely related to the Aleksandrov-Rassias problems, the main subject of this book. He published numerous papers and books in the fields of measure theory, fractal geometry, number theory, classical analysis, Euclidean geometry, discrete mathematics, differential equations, and functional equations.