Matches in SemOpenAlex for { <https://semopenalex.org/work/W1969137912> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W1969137912 abstract "In this paper we investigate the global behavior of proper holomorphic maps f from the unit disc U={|z|<1} to C^2. The fact that U is transcendental imposes certain restrictions on the image f(U). For instance, f(U) cannot be contained in any proper complex cone in C^2 since this would force it to be algebraic. On the other hand, we show that a real cone in C^2 with axis R^2 contains the image of a proper holomorphic map f from U to C^2 if and only if the angle of the cone is larger than pi/2. We also construct maps f as above whose images avoid both coordinate axes in C^2. Equivalently, we construct a pair of positive harmonic functions u, v on U such that max{u(z),v(z)} tends to plus infinity when z tends to the boundary of U. Furthermore we show that the components f_1, f_1 of a proper holomorphic map from U to C^2, as well as polynomial and certain rational functions of f_1 and f_2, have the property that their essential range at any boundary point of U omits at most a polar set in C." @default.
- W1969137912 created "2016-06-24" @default.
- W1969137912 creator A5007749653 @default.
- W1969137912 creator A5043857437 @default.
- W1969137912 date "2001-01-04" @default.
- W1969137912 modified "2023-09-27" @default.
- W1969137912 title "Proper holomorphic discs in C^2" @default.
- W1969137912 hasPublicationYear "2001" @default.
- W1969137912 type Work @default.
- W1969137912 sameAs 1969137912 @default.
- W1969137912 citedByCount "0" @default.
- W1969137912 crossrefType "posted-content" @default.
- W1969137912 hasAuthorship W1969137912A5007749653 @default.
- W1969137912 hasAuthorship W1969137912A5043857437 @default.
- W1969137912 hasConcept C11413529 @default.
- W1969137912 hasConcept C114614502 @default.
- W1969137912 hasConcept C115961682 @default.
- W1969137912 hasConcept C134306372 @default.
- W1969137912 hasConcept C154945302 @default.
- W1969137912 hasConcept C188370112 @default.
- W1969137912 hasConcept C202444582 @default.
- W1969137912 hasConcept C204575570 @default.
- W1969137912 hasConcept C2524010 @default.
- W1969137912 hasConcept C30014739 @default.
- W1969137912 hasConcept C33923547 @default.
- W1969137912 hasConcept C41008148 @default.
- W1969137912 hasConcept C62354387 @default.
- W1969137912 hasConcept C90119067 @default.
- W1969137912 hasConcept C9376300 @default.
- W1969137912 hasConceptScore W1969137912C11413529 @default.
- W1969137912 hasConceptScore W1969137912C114614502 @default.
- W1969137912 hasConceptScore W1969137912C115961682 @default.
- W1969137912 hasConceptScore W1969137912C134306372 @default.
- W1969137912 hasConceptScore W1969137912C154945302 @default.
- W1969137912 hasConceptScore W1969137912C188370112 @default.
- W1969137912 hasConceptScore W1969137912C202444582 @default.
- W1969137912 hasConceptScore W1969137912C204575570 @default.
- W1969137912 hasConceptScore W1969137912C2524010 @default.
- W1969137912 hasConceptScore W1969137912C30014739 @default.
- W1969137912 hasConceptScore W1969137912C33923547 @default.
- W1969137912 hasConceptScore W1969137912C41008148 @default.
- W1969137912 hasConceptScore W1969137912C62354387 @default.
- W1969137912 hasConceptScore W1969137912C90119067 @default.
- W1969137912 hasConceptScore W1969137912C9376300 @default.
- W1969137912 hasLocation W19691379121 @default.
- W1969137912 hasOpenAccess W1969137912 @default.
- W1969137912 hasPrimaryLocation W19691379121 @default.
- W1969137912 hasRelatedWork W1532270476 @default.
- W1969137912 hasRelatedWork W1593943913 @default.
- W1969137912 hasRelatedWork W1971025151 @default.
- W1969137912 hasRelatedWork W2039093232 @default.
- W1969137912 hasRelatedWork W2041739991 @default.
- W1969137912 hasRelatedWork W2042279657 @default.
- W1969137912 hasRelatedWork W2129175520 @default.
- W1969137912 hasRelatedWork W2158372301 @default.
- W1969137912 hasRelatedWork W2237384732 @default.
- W1969137912 hasRelatedWork W2291993526 @default.
- W1969137912 hasRelatedWork W2339864038 @default.
- W1969137912 hasRelatedWork W253692439 @default.
- W1969137912 hasRelatedWork W2794858802 @default.
- W1969137912 hasRelatedWork W2798266874 @default.
- W1969137912 hasRelatedWork W2807277444 @default.
- W1969137912 hasRelatedWork W2950519520 @default.
- W1969137912 hasRelatedWork W2953142193 @default.
- W1969137912 hasRelatedWork W2953332296 @default.
- W1969137912 hasRelatedWork W2963619486 @default.
- W1969137912 hasRelatedWork W3099538223 @default.
- W1969137912 isParatext "false" @default.
- W1969137912 isRetracted "false" @default.
- W1969137912 magId "1969137912" @default.
- W1969137912 workType "article" @default.