Charles Loewner

Charles Loewner
Charles Loewner in '63
Born	29 May 1893(1893-05-29) Lány, Bohemia
Died	8 January 1968(1968-01-08) (aged 74) Stanford, California
Nationality	American
Fields	Mathematics
Institutions	Stanford University Syracuse University University of Prague
Alma mater	University of Prague
Doctoral advisor	Georg Alexander Pick
Doctoral students	Lipman Bers Adriano Garsia Pao Ming Pu

Charles Loewner (29 May 1893 – 8 January 1968) was an American mathematician. His name was Karel Löwner in Czech and Karl Löwner in German.

Loewner received his Ph.D. from the University of Prague in 1917 under supervision of Georg Pick. One of his central mathematical contributions is the proof of the Bieberbach conjecture in the first highly nontrivial case of the third coefficient. He worked at the University of Berlin, 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.

Loewner's torus inequality

In 1949 Loewner proved his torus inequality, to the effect that every metric on the 2-torus satisfies the optimal inequality

$\operatorname{sys}^2 \leq \frac{2}{\sqrt{3}} \operatorname{area} (\mathbb T^2),$

where sys is its 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 $\mathbb C$.

Book by Loewner

• 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.

See also

• Schramm–Loewner evolution
• Loop-erased random walk
• Systolic geometry

References

• Berger, Marcel: À l'ombre de Loewner. (French) Ann. Sci. École Norm. Sup. (4) 5 (1972), 241--260.
• 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.

External links

• Stanford memorial resolution
• Charles Loewner at the Mathematics Genealogy Project.
• O'Connor, John J.; Robertson, Edmund F., "Charles Loewner", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Loewner.html .

Persondata
Name	Loewner, Charles
Alternative names
Short description
Date of birth	29 May 1893
Place of birth	Lány, Bohemia
Date of death	8 January 1968
Place of death	Stanford, California

This article about a European mathematician is a stub. You can help Wikipedia by expanding it.v · http://en.wikipedia.org/wiki/Charles_Loewner" Wikimedia Foundation. 2010. Игры ⚽ Нужен реферат? The Piano Man's Daughter (film) The Mainspring of Human Progress Look at other dictionaries: Charles Loewner — C. Loewner à droite (inconnu à gauche) en 1927 (coll. MFO) Naissance …   Wikipédia en Français Charles Loewner — Charles Löwner, eigentlich Karel Löwner, deutsch auch Karl Löwner, (* 29. Mai 1893 in Lany; † 8. Januar 1968 in Stanford (Kalifornien)) war ein tschechisch US amerikanischer Mathematiker, der sich vor allem mit Funktionentheorie und Analysis… …   Deutsch Wikipedia Loewner — Charles Löwner, eigentlich Karel Löwner, deutsch auch Karl Löwner, (* 29. Mai 1893 in Lany; † 8. Januar 1968 in Stanford (Kalifornien)) war ein tschechisch US amerikanischer Mathematiker, der sich vor allem mit Funktionentheorie und Analysis… …   Deutsch Wikipedia Loewner's torus inequality — In differential geometry, Loewner s torus inequality is an inequality due to Charles Loewner for the systole of an arbitrary Riemannian metric on the 2 torus.tatementIn 1949 Charles Loewner proved that every metric on the 2 torus mathbb T^2… …   Wikipedia Charles M. Newman — Charles Michael Chuck Newman (born 1 March 1946) is a mathematician and a physicist at the Courant Institute of Mathematical Sciences of New York University. He works in the fields of mathematical physics, statistical mechanics, and probability… …   Wikipedia Schramm–Loewner evolution — In probability theory, Schramm–Loewner evolution, also known as stochastic Loewner evolution or SLE, is a conformally invariant stochastic process. It is a family of random planar curves that are generated by solving Charles Loewner s… …   Wikipedia Inégalité torique de Loewner — En géométrie différentielle, l inégalité torique de Loewner est une inégalité établie par le mathématicien américain Charles Loewner. Elle relie la systole et la superficie d une métrique riemannienne quelconque d un tore de dimension 2.… …   Wikipédia en Français Introduction to systolic geometry — Systolic geometry is a branch of differential geometry, a field within mathematics, studying problems such as the relationship between the area inside a closed curve C , and the length or perimeter of C . Since the area A may be small while the… …   Wikipedia Pao Ming Pu — (the form of his name he used in Western languages, although the Wade Giles transliteration would be Pu Baoming; Chinese: 蒲保明 also named 蒲保民; pinyin: Pú Bǎomíng; Aug. 1910– Feb. 22, 1988), was a mathematician born in Jintang County, Sichuan,… …   Wikipedia Systolic geometry — In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner, and developed by Mikhail Gromov and others, in its arithmetic, ergodic, and topological manifestations.… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”