Hyperplane Singularities of Analytic Functions of Several Complex Variables

1997 ◽  
Vol 4 (2) ◽  
pp. 163-184
Author(s):  
M. Shubladze
Keyword(s):  
Critical Points ◽  
Analytic Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Algebraic Expression ◽  
Isolated Singularities ◽  
Milnor Fibre ◽  
New Class

Abstract A new class of non-isolated singularities called hyperplane singularities is introduced. Special deformations with simplest critical points are constructed and an algebraic expression for the number of Morse points is given. The topology of the Milnor fibre is completely studied.

Elementarfunktionen Auf Riemannschen Flächen Als Hilfsmittel Für Die Funktionentheorie MEHRERER Veränderlichen

1950 ◽  
Vol 2 ◽  
pp. 152-165 ◽  
Author(s):  
Heinrich Behnke ◽  
Karl Stein
Keyword(s):  
Direct Product ◽  
Analytic Functions ◽  
Riemann Surfaces ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Continuity Theorem ◽  
Poles And Zeros ◽  
The Given

In the present paper, the authors extend the Cousin theorems and the continuity theorem, using some previous results on analytic functions connected with open Riemann surfaces.The Cousin theorems, concerning the existence of analytic functions of several complex variables with prescribed poles and zeros in a given domain, have been generalized in various manners, but only in the case where the domain is schlicht. The authors proceed to the case where the given domain is the direct product of n open Riemann surfaces. They prove the following two theorems.

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