Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Riemann mapping theorem
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
==References== *{{citation|last=Ahlfors|first= Lars V.|author-link=Lars Ahlfors|title=Complex analysis. An introduction to the theory of analytic functions of one complex variable|edition=3rd|series= International Series in Pure and Applied Mathematics|publisher= McGraw-Hill|year= 1978|isbn= 0070006571}} *{{citation|last=Beardon|first= Alan F.|author-link=Alan Frank Beardon|title=Complex analysis.The argument principle in analysis and topology|publisher= John Wiley & Sons|year= 1979|isbn= 0471996718}} *{{citation|last=Bell|first=Steven R.|title= The Cauchy transform, potential theory, and conformal mapping|series= Studies in Advanced Mathematics|publisher= CRC Press|year= 1992|isbn=0-8493-8270-X}} *{{citation|last1=Berenstein|first1=Carlos A.|last2=Gay|first2= Roger|title=Complex variables. An introduction |series= Graduate Texts in Mathematics|volume= 125|publisher= [[Springer-Verlag]]|year= 1991|isbn= 0387973494}} *{{citation|last=Carathéodory|first=C.|title=Untersuchungen über die konformen Abbildungen von festen und veranderlichen Gebieten|journal=Mathematische Annalen|volume=72|pages=107–144|year=1912|doi=10.1007/bf01456892 |s2cid=115544426 |url=https://zenodo.org/record/1428282}} *{{citation|author-link=John B. Conway|last=Conway|first= John B.| year=1978|title=Functions of one complex variable|publisher=[[Springer-Verlag]]|isbn=0-387-90328-3}} *{{citation|first=John B.|last= Conway|author-link=John B. Conway|year= 1995|title=Functions of one complex variable II|publisher=[[Springer-Verlag]]| isbn= 0-387-94460-5}} *{{citation|last=Duren|first=P. L.|author-link=Peter Duren|chapter=Extremal problems for univalent functions|title= Aspects of contemporary complex analysis|pages= 181–208|publisher= Academic Press|year= 1980|isbn=9780121259501|editor1-first=D.A.|editor1-last=Brannan|editor2-first=J.G.|editor2-last=Clunie}} *{{citation|last=Duren|first=P. L.|author-link=Peter Duren|title=Univalent functions|series=Grundlehren der Mathematischen Wissenschaften|volume= 259|publisher= Springer-Verlag|year= 1983|isbn= 0-387-90795-5}} *{{citation|last=Gamelin|first=Theodore W.|author-link=Theodore Gamelin|title= Complex analysis|series= Undergraduate Texts in Mathematics|publisher= Springer|year= 2001|isbn=0-387-95069-9}} *{{citation|last=Goluzin|first=G. M.|title= Geometric theory of functions of a complex variable|series=Translations of Mathematical Monographs|volume= 26|publisher= American Mathematical Society|year= 1969}} *{{Citation | last=Gray | first=Jeremy | author-link=Jeremy Gray | title=On the history of the Riemann mapping theorem | url=http://www.math.stonybrook.edu/~bishop/classes/math401.F09/GrayRMT.pdf | mr=1295591 | year=1994 | journal=Rendiconti del Circolo Matematico di Palermo. Serie II. Supplemento | issue=34 | pages=47–94}} *{{citation|last1=Greene|first1=Robert E.|author-link1=Robert Everist Greene|last2=Kim|first2=Kang‑Tae|author-link2=Kang-Tae Kim|title=The Riemann mapping theorem from Riemann's viewpoint|journal=Complex Analysis and Its Synergies|year=2017|volume=3 |doi=10.1186/s40627-016-0009-7|doi-access=free|arxiv=1604.04071}} *{{citation|last=Grötzsch|first= Herbert|year=1932|author-link=Herbert Grötzsch|title= Über das Parallelschlitztheorem der konformen Abbildung schlichter Bereiche|journal= Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig, Mathematisch-Physische Klasse |volume=84|pages=15–36|lang=de|zbl= 0005.06802}} *{{citation|last=Grunsky|first= Helmut|title=Lectures on theory of functions in multiply connected domains|series=Studia Mathematica| volume= 4| publisher=Vandenhoeck & Ruprecht|year= 1978|isbn= 978-3-525-40142-2}} *{{citation|last= Jänich|first= Klaus|title= Funktionentheorie. Eine Einführung|edition=3rd|series= Springer-Lehrbuch|publisher= [[Springer-Verlag]] |year= 1993|isbn= 3540563377|lang=de}} *{{citation|last=Jenkins|first= James A.|title=Univalent functions and conformal mapping.|series=Ergebnisse der Mathematik und ihrer Grenzgebiete|volume= 18|publisher= [[Springer-Verlag]]|year= 1958}} *{{citation|last=Kodaira|first=Kunihiko|author-link=Kunihiko Kodaira|title= Complex analysis|series=Cambridge Studies in Advanced Mathematics|volume= 107|publisher= Cambridge University Press|year= 2007|isbn= 9780521809375}} *{{citation|author-link=Steven G. Krantz|last=Krantz|first=Steven G.|year= 2006|title=Geometric Function Theory| chapter= Riemann Mapping Theorem and its Generalizations|pages=83–108|publisher=[[Birkhäuser]]|isbn=0-8176-4339-7}} *{{citation|author-link1=Akhlesh Lakhtakia|last1=Lakhtakia|first1=Akhlesh|last2=Varadan|first2=Vijay K.|last3=Messier|first3=Russell|author-link4=Vasundara Varadan|last4=Varadan|first4=Vasundara|year=1987|title=Generalisations and randomisation of the plane Koch curve|journal=Journal of Physics A: Mathematical and General|volume=20|issue=11|pages=3537–3541|doi=10.1088/0305-4470/20/11/052}} *{{Citation | last=Nehari | first=Zeev |author-link=Zeev Nehari| title=Conformal mapping | year=1952 | publisher=[[Dover Publications]] |isbn=9780486611372 }} *{{citation | author-link= W. F. Osgood|last1=Osgood | first1=W. F. | title=On the Existence of the Green's Function for the Most General Simply Connected Plane Region | jstor=1986285 | publisher=[[American Mathematical Society]] | location=Providence, R.I. | jfm=31.0420.01 | year=1900 | journal=[[Transactions of the American Mathematical Society]] | issn=0002-9947 | volume=1 | issue=3 | pages=310–314 | doi=10.2307/1986285}} *{{citation|title=Zum Parallelschlitztheorm unendlich- vielfach zusammenhängender Gebiete |last=de Possel|first= René|author-link=René de Possel|journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse |year= 1931|pages=199−202|lang=de|url=https://gdz.sub.uni-goettingen.de/id/PPN252457811_1931?tify={%22pages%22:[203],%22panX%22:0.758,%22panY%22:0.57,%22view%22:%22export%22,%22zoom%22:0.501} }} *{{citation |author-link=Reinhold Remmert |last=Remmert |first=Reinhold |year=1998 |title=Classical topics in complex function theory |translator=[[Leslie M. Kay]] |publisher=[[Springer-Verlag]] |isbn=0-387-98221-3}} *{{citation|author-link=Bernhard Riemann|last=Riemann|first=Bernhard| year=1851|url=http://www.emis.de/classics/Riemann/Grund.pdf|title= Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse|location= Göttingen|lang=de}} *{{citation|last=Schiff|first= Joel L.|title=Normal families|series=Universitext|publisher= [[Springer-Verlag]]|year= 1993|isbn= 0387979670}} *{{citation|last=Schober|first=Glenn|title=Univalent functions—selected topics|series=Lecture Notes in Mathematics|volume=478| publisher=[[Springer-Verlag]]|year= 1975|pages=181–190|chapter=Appendix C. Schiffer's boundary variation and fundamental lemma}} *{{Citation | last1=Walsh | first1=J. L. | author-link=Joseph L. Walsh | title=History of the Riemann mapping theorem | jstor=2318448 | mr=0323996 | year=1973 | journal=[[American Mathematical Monthly|The American Mathematical Monthly]] | issn=0002-9890 | volume=80 | issue=3 | pages=270–276 | doi=10.2307/2318448}}
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)