{"title":"Junjiro Noguchi","description":null,"products":[{"product_id":"prospects-in-complex-geometry-book-junjiro-noguchi-9783540540533","title":"Prospects in Complex Geometry","description":"In the Teichmuller theory of Riemann surfaces, besides the classical theory of quasi-conformal mappings, vari- ous approaches from differential geometry and algebraic geometry have merged in recent years. Thus the central subject of Complex Structure was a timely choice for the joint meetings in Katata and Kyoto in 1989. The invited participants exchanged ideas on different approaches to related topics in complex geometry and mapped out the prospects for the next few years of research.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52145339695377,"sku":"NLS9783540540533","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540540533.jpg?v=1785795005"},{"product_id":"basic-oka-theory-in-several-complex-variables-book-junjiro-noguchi-9789819720552","title":"Basic Oka Theory in Several Complex Variables","description":"\u003cp\u003eThis book provides a new, comprehensive, and self-contained account of Oka theory as an introduction to function theory of several complex variables, mainly concerned with the Three Big Problems (Approximation, Cousin, Pseudoconvexity) that were solved by Kiyoshi Oka and form the basics of the theory. The purpose of the volume is to serve as a textbook in lecture courses right after complex function theory of one variable. The presentation aims to be readable and enjoyable both for those who are beginners in mathematics and for researchers interested in complex analysis in several variables and complex geometry.\u003c\/p\u003e\n\n\u003cp\u003eThe nature of the present book is evinced by its approach following Oka’s unpublished five papers of 1943 with his guiding methodological principle termed the “Joku-Iko Principle”, where historically the Pseudoconvexity Problem (Hartogs, Levi) was first solved in all dimensions, even for unramified Riemann domains as well.\u003c\/p\u003e\n\n\u003cp\u003eThe method that is used in the book is elementary and direct, not relying on the cohomology theory of sheaves nor on the \u003cem\u003eL\u003c\/em\u003e2-∂-bar method, but yet reaches the core of the theory with the complete proofs.\u003c\/p\u003e\n\n\u003cp\u003eTwo proofs for Levi’s Problem are provided: One is Oka’s original with the Fredholm integral equation of the second kind combined with the Joku-Iko Principle, and the other is Grauert’s by the well-known “bumping-method” with L. Schwartz’s Fredholm theorem, of which a self-contained, rather simple and short proof is given. The comparison of them should be interesting even for specialists.\u003c\/p\u003e\n\n\u003cp\u003eIn addition to the Three Big Problems, other basic material is dealt with, such as Poincaré’s non-biholomorphism between balls and polydisks, the Cartan–Thullen  theorem on holomorphic convexity, Hartogs’ separate analyticity, Bochner’s tube theorem, analytic interpolation, and others.\u003c\/p\u003e\n\n\u003cp\u003eIt is valuable for students and researchers alike to look into the original works of Kiyoshi Oka, which are not easy to find in books or monographs.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":52151868424465,"sku":"NGR9789819720552","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789819720552.jpg?v=1785839870"},{"product_id":"analytic-function-theory-of-several-variables-book-junjiro-noguchi-9789811002892","title":"Analytic Function Theory of Several Variables","description":"This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appears much later.The present book, consisting of nine chapters, gives complete treatments of the following items: Coherence of sheaves of holomorphic functions (Chap.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52431654879505,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52431655600401,"sku":"NLS9789811002892","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789811002892.jpg?v=1759173138"},{"product_id":"analytic-function-theory-of-several-variables-book-junjiro-noguchi-9789811091247","title":"Analytic Function Theory of Several Variables","description":"The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert's two volumes, GL227(236) (\u003ci\u003eTheory of Stein spaces\u003c\/i\u003e) and GL265 (\u003ci\u003eCoherent analytic sheaves\u003c\/i\u003e) with a lowering of the level for novice graduate students (here, Grauert's direct image theorem is limited to the case of finite maps).The core of the theory is \"Oka's Coherence\", found and proved by Kiyoshi Oka. It is indispensable, not only in the study of complex analysis and complex geometry, but also in a large area of modern mathematics. In this book, just after an introductory chapter on holomorphic functions (Chap. 1), we prove Oka's First Coherence Theorem for holomorphic functions in Chap. 2. This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appears much later.The present book, consisting of nine chapters, gives complete treatments of the following items: Coherence of sheaves of holomorphic functions (Chap. 2); Oka–Cartan's Fundamental Theorem (Chap. 4); Coherence of ideal sheaves of complex analytic subsets (Chap. 6); Coherence of the normalization sheaves of complex spaces (Chap. 6); Grauert's Finiteness Theorem (Chaps. 7, 8); Oka's Theorem for Riemann domains (Chap. 8). The theories of sheaf cohomology and domains of holomorphy are also presented (Chaps. 3, 5). Chapter 6 deals with the theory of complex analytic subsets. Chapter 8 is devoted to the applications of formerly obtained results, proving Cartan–Serre's Theorem and Kodaira's Embedding Theorem. In Chap. 9, we discuss the historical development of \"Coherence\".It is difficult to find a book at this level that treats all of the above subjects in a completely self-contained manner. In the present volume, a number of classical proofs are improved and simplified, so that the contents are easily accessible for beginning graduate students.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52583557497105,"sku":"NLS9789811091247","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789811091247.jpg?v=1761047332"},{"product_id":"nevanlinna-theory-in-several-complex-variables-and-diophantine-approximation-book-junjiro-noguchi-9784431562139","title":"Nevanlinna Theory in Several Complex Variables and Diophantine Approximation","description":"\u003cp\u003eThe aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers.\u003c\/p\u003e\u003cp\u003eThis book with nine chapters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 to the current state of research.\u003c\/p\u003e\u003cp\u003eChapter 2 presents the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension is described. In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory.\u003c\/p\u003e\u003cp\u003eEstablishing such a Second Main Theorem for entire curves in general complex algebraic varieties isa wide-open problem. In Chap. 4, the Cartan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraic varieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of Noguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to the notion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are discussed in Chap. 7.\u003c\/p\u003e\u003cp\u003eIn the last two chapters Diophantine approximation theory is dealt with from the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is discussed. Finally, in Chap. 9, the theorems of Roth, Schmidt, Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, 6, and 7.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52634072580369,"sku":"NLS9784431562139","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9784431562139.jpg?v=1786873641"},{"product_id":"nevanlinna-theory-in-several-complex-variables-and-diophantine-approximation-book-junjiro-noguchi-9784431545705","title":"Nevanlinna Theory in Several Complex Variables and Diophantine Approximation","description":"\u003cp\u003eThe aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers.\u003c\/p\u003e\u003cp\u003eThis book with nine chapters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 to the current state of research.\u003c\/p\u003e\u003cp\u003eChapter 2 presents the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension is described. In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory.\u003c\/p\u003e\u003cp\u003eEstablishing such a Second Main Theorem for entire curves in general complex algebraic varieties isa wide-open problem. In Chap. 4, the Cartan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraic varieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of Noguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to the notion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are discussed in Chap. 7.\u003c\/p\u003e\u003cp\u003eIn the last two chapters Diophantine approximation theory is dealt with from the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is discussed. Finally, in Chap. 9, the theorems of Roth, Schmidt, Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, 6, and 7.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52664699552017,"sku":"NLS9784431545705","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9784431545705.jpg?v=1762275310"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-junjiro-noguchi.oembed","provider":"World of Books ","version":"1.0","type":"link"}