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| {{Infobox scientist
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| | name = Charles Loewner
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| | image = Loewner63.jpg
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| | image_size = 200px
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| | caption = Charles Loewner in '63
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| | birth_date = {{birth date|1893|05|29|df=y}}
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| | birth_place = [[Lány (Kladno District)|Lány]], [[Kingdom of Bohemia|Bohemia]]
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| | death_date = {{death date and age|1968|01|08|1893|05|29|df=y}}
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| | death_place = [[Stanford, California|Stanford]], [[California]]
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| | nationality = [[USA|American]]
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| | fields = [[Mathematics]]
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| | workplaces = [[Stanford University]]<br>[[Syracuse University]]<br>[[Karl-Ferdinands-Universität|University of Prague]]
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| | alma_mater = Karl-Ferdinands-Universität
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| | doctoral_advisor = [[Georg Alexander Pick]]
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| | doctoral_students = [[Lipman Bers]]<br>[[Adriano Garsia]]<br>[[Pao Ming Pu]]
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| | known_for =
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| | awards =
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| }}
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| '''Charles Loewner''' (29 May 1893 – 8 January 1968) was an [[United States|American]] [[mathematician]]. His name was '''Karel Löwner''' in Czech and '''Karl Löwner''' in German.
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| Karl Loewner was born into a Jewish family in Lany, about 30 km from Prague, where his father Sigmund Löwner was a store owner.<ref>[http://www-history.mcs.st-andrews.ac.uk/Biographies/Loewner.html Loewner Biography]</ref><ref>[http://www.ams.org/bookstore/pspdf/surv-137-prev.pdf 2.2 Charles Loewner]</ref>
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| Loewner received his Ph.D. from the [[Karl-Ferdinands-Universität|University of Prague]] in 1917 under supervision of [[Georg Alexander Pick|Georg Pick]].
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| One of his central mathematical contributions is the proof of the [[De Branges' theorem|Bieberbach conjecture]] in the first highly nontrivial case of the third coefficient. The technique he introduced, the [[Loewner differential equation]], has had far-reaching implications in [[geometric function theory]]; it was used in the final solution of the Bieberbach conjecture by [[Louis de Branges]] in 1985. Loewner worked at the [[University of Berlin]], [[Karl-Ferdinands-Universität|University of Prague]], [[Louisville University]], [[Brown University]], [[Syracuse University]] and eventually at [[Stanford University]]. His students include [[Lipman Bers]], [[Roger A. Horn]], [[Adriano Garsia]], and [[P. M. Pu]].
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| ==Loewner's torus inequality==
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| In 1949 Loewner proved his [[Loewner's torus inequality|torus inequality]], to the effect that every metric on the 2-torus satisfies the optimal inequality
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| :<math> \operatorname{sys}^2 \leq \frac{2}{\sqrt{3}} \operatorname{area} (\mathbb T^2),</math>
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| where sys is its [[Systolic geometry|systole]]. The boundary case of equality is attained if and only if the metric is flat and homothetic to the so-called ''equilateral torus'', i.e. torus whose group of deck transformations is precisely the [[hexagonal lattice]] spanned by the cube roots of unity in <math>\mathbb C</math>.
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| ==Book by Loewner==
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| *Loewner, C.: Theory of continuous groups. Notes by H. Flanders and M. Protter. Mathematicians of Our Time 1, The MIT Press, Cambridge, Mass.—London, 1971.
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| ==See also==
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| * [[Loewner differential equation]]
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| * [[Schramm–Loewner evolution]]
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| * [[Loop-erased random walk]]
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| * [[Systolic geometry]]
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| ==References==
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| *[[Marcel Berger|Berger, Marcel]]: À l'ombre de Loewner. (French) Ann. Sci. École Norm. Sup. (4) 5 (1972), 241–260.
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| *Loewner, Charles; Nirenberg, Louis: Partial differential equations invariant under conformal or projective transformations. Contributions to analysis (a collection of papers dedicated to Lipman Bers), pp. 245–272. Academic Press, New York, 1974.
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| {{Reflist}}
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| ==External links==
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| * [http://histsoc.stanford.edu/pdfmem/LoewnerC.pdf Stanford memorial resolution]
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| *{{MathGenealogy |id=11755}}
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| *{{MacTutor Biography|id=Loewner}}
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| {{Authority control|VIAF=29598962|LCCN=n/88/114777|GND=118838660}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Loewner, Charles
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Czech-American mathematician
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| | DATE OF BIRTH = 29 May 1893
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| | PLACE OF BIRTH = [[Lány (Kladno District)|Lány]], [[Bohemia]]
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| | DATE OF DEATH = 8 January 1968
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| | PLACE OF DEATH = [[Stanford, California|Stanford]], [[California]]
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| }}
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| {{DEFAULTSORT:Loewner, Charles}}
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| [[Category:1893 births]]
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| [[Category:1968 deaths]]
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| [[Category:20th-century mathematicians]]
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| [[Category:American mathematicians]]
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| [[Category:Czech mathematicians]]
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| [[Category:Mathematical analysts]]
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| [[Category:Jewish scientists]]
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