Kang-Tae Kim - Böcker

This work examines a rich tapestry of themes and concepts that provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space. At once authoritative and accessible, this text touches upon many important parts of modern mathematics: complex geometry, Finsler metrics, Bergman and Kahler geometry, curvatures, differential invariants, boundary asymptotics of geometries, group actions, and moduli spaces.This text can serve as a "coming of age" book for a graduate student who has completed at least one semester or more of complex analysis, and will be most welcomed by analysts and geometers engaged in current research.

This volume includes 28 chapters by authors who are leading researchers of the world describing many of the up-to-date aspects in the field of several complex variables (SCV). These contributions are based upon their presentations at the 10th Korean Conference on Several Complex Variables (KSCV10), held as a satellite conference to the International Congress of Mathematicians (ICM) 2014 in Seoul, Korea.SCV has been the term for multidimensional complex analysis, one of the central research areas in mathematics. Studies over time have revealed a variety of rich, intriguing, new knowledge in complex analysis and geometry of analytic spaces and holomorphic functions which were "hidden" in the case of complex dimension one. These new theories have significant intersections with algebraic geometry, differential geometry, partial differential equations, dynamics, functional analysis and operator theory, and sheaves and cohomology, as well as the traditional analysis of holomorphic functions in all dimensions.This book is suitable for a broad audience of mathematicians at and above the beginning graduate-student level. Many chapters pose open-ended problems for further research, and one in particular is devoted to problems for future investigations.

These contributions are based upon their presentations at the 10th Korean Conference on Several Complex Variables (KSCV10), held as a satellite conference to the International Congress of Mathematicians (ICM) 2014 in Seoul, Korea.SCV has been the term for multidimensional complex analysis, one of the central research areas in mathematics.

The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date. This volume of lecture notes focuses on its differential geometric developments by several excellent authors including, but not limited to, L Ahlfors, S S Chern, Y C Lu, S T Yau and H L Royden.This volume can be approached by a reader who has basic knowledge on complex analysis and Riemannian geometry. It contains major historic differential geometric generalizations on Schwarz's Lemma and provides the necessary information while making the whole volume as concise as ever.

This volume presents a collection of research papers and survey articles by participants from two significant conferences on several complex variables (SCV) held at POSTECH in 2022. SCV, a central research area in mathematics, focuses on holomorphic functions of several variables, the geometry of analytic spaces, and its intersection with fields such as differential geometry, algebraic geometry, functional analysis, and operator theory.The first conference, The Conference on Complex Geometric Analysis, took place in January 2022 to celebrate the 65th birthday of Professor Kang-Tae Kim, a leading figure in SCV. The second, held in July 2022, was The POSTECH Conference 2022 on Complex Analytic Geometry, a joint event that included The 14th Korean Symposium of Several Complex Variables and The 28th International Conference on Finite and Infinite Dimensional Complex Analysis and Applications. Both conferences attracted over 50 prominent researchers who gave lectures on the latest developments in the field. This volume serves as a testament to their contributions and the ongoing advancements in SCV research.