Get Value Distribution Theory and Related Topics (Advances in PDF

By Grigor A. Barsegian, Ilpo Laine, Chung-Chun Yang

ISBN-10: 1402079508

ISBN-13: 9781402079504

ISBN-10: 1402079516

ISBN-13: 9781402079511

The Nevanlinna thought of worth distribution of meromorphic capabilities, one of many milestones of advanced research over the last century, used to be c- ated to increase the classical effects in regards to the distribution of of whole features to the extra basic surroundings of meromorphic services. afterward, the same reasoning has been utilized to algebroid capabilities, subharmonic services and meromorphic features on Riemann surfaces in addition to to - alytic services of a number of complicated variables, holomorphic and meromorphic mappings and to the idea of minimum surfaces. additionally, numerous appli- tions of the speculation were exploited, together with complicated differential and sensible equations, advanced dynamics and Diophantine equations. the most emphasis of this assortment is to direct consciousness to a few lately built novel principles and generalizations that relate to the - velopment of worth distribution conception and its purposes. particularly, we suggest a up to date conception that replaces the traditional attention of counting inside a disc through an research in their geometric destinations. one other such instance is gifted via the generalizations of the second one major theorem to raised dimensional instances through the use of the jet conception. additionally, s- ilar principles it sounds as if can be utilized to numerous similar components to boot, resembling to partial differential equations and to differential geometry. certainly, each one of these purposes return to the matter of interpreting zeros of sure advanced or actual features, which means in reality to enquire point units or point surfaces.

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6), we conclude that at least some of the quantities should be large as well. Now we want to investigate Problem 20. What can be said about the interpolation problem above for non-algebraic curves Field 21: Transfer of concepts and results of complex analysis in differentia l geometry We now introduce the notion of in differential geometry. Let M be a smooth surface in whose Gaussian mapping G transfers M onto a set G(M) on the Riemann sphere S. 5 5 The Gaussian mapping G maps each point of M onto the sphere S with radius equal to 1 such that the normal to M at the point and the normal to the sphere at the Gaussian image coincide.

From mathematical points of view it would be highly interesting to obtain analogs of main results related to Gamma-lines. 3. 1). 1) in a subdomain of D. 2). We now add here a short survey of similar problems: A particular case interesting in applied mathematics. From the point of view applications, investigating of generalized seems to be even more promising than in the classical case. The matter is that, unlike to the classical case of of a complex function have important interpretations in very different applied situations.

This should, in turn, imply “almost analytical” properties in a neighborhood of infinity. 1. 2. What can be said about “almost analytical” properties of solutions of or of in terms of or Field 29: Topological properties of multi-valued functions and multi-valued solutions of some classes of complex differential equations We first remark that this section is essentially based on [26]. Considering differential equations, or systems of differential equations from a global point of view it is natural to be interested in the description of global properties of solutions in maximally large domains of definition.

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Value Distribution Theory and Related Topics (Advances in Complex Analysis and Its Applications) by Grigor A. Barsegian, Ilpo Laine, Chung-Chun Yang

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