Hermann Schwarz
Hermann Schwarz | |
|---|---|
Göttingen University | |
| Doctoral advisor | Karl Weierstrass Ernst Kummer |
| Doctoral students | Lipót Fejér Harris Hancock Gerhard Hessenberg Paul Koebe Leon Lichtenstein Heinrich Maschke Robert Remak Rudolf Rothe Theodor Vahlen Ernst Zermelo |
Karl Hermann Amandus Schwarz (German: [ˈhɛʁman ˈʃvaʁts]; 25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis.
Life
Schwarz was born in
Schwarz originally studied
Work
Schwarz's works include Bestimmung einer speziellen Minimalfläche, which was crowned by the Berlin Academy in 1867 and printed in 1871, and Gesammelte mathematische Abhandlungen (1890).
Among other things, Schwarz improved the proof of the Riemann mapping theorem,[6] developed a special case of the Cauchy–Schwarz inequality, and gave a proof that the ball has less surface area than any other body of equal volume.[7] His work on the latter allowed Émile Picard to show solutions of differential equations exist (the Picard–Lindelöf theorem).[3]
In 1892 he became a member of the
His name is attached to many ideas in mathematics,[2] including the following:
- Abstract additive Schwarz method
- Additive Schwarz method
- Schwarz alternating method
- Schwarzian derivative
- Schwarz function
- Schwarz lantern
- Schwarz lemma
- Schwarz's list
- Schwarz minimal surface
- Schwarz theorem(also known as Clairaut's theorem)
- Schwarz integral formula
- Schwarz–Christoffel mapping
- Schwarz–Ahlfors–Pick theorem
- Schwarz reflection principle
- Schwarz triangle
- Schwarz triangle function
- Cauchy–Schwarz inequality
- Theorem of Pohlke and Schwarz
Publications
- Schwarz, H. A. (1871), Bestimmung einer speziellen Minimalfläche, Dümmler
- Schwarz, H. A. (1972) [1890], Gesammelte mathematische Abhandlungen. Band I, II, Bronx, N.Y.: AMS Chelsea Publishing, MR 0392470
Notes
- . Retrieved 7 July 2021.
- ^ ISBN 9783319108704.
- ^ a b O'Connor, J. J.; Robertson, E. F. "Schwarz biography". www-gap.dcs.st-and.ac.uk. The MacTutor History of Mathematics. Archived from the original on 5 June 2016. Retrieved 22 May 2016.
- ^ a b "The Mathematics Genealogy Project – Hermann Schwarz". www.genealogy.math.ndsu.nodak.edu. Retrieved 22 May 2016.
- ^ ISBN 9789814282291.
- arXiv:math/0305022.
- ^ Schwarz, Hermann Amandus (1884). "Proof of the theorem that the ball has less surface area than any other body of the same volume". News of the Royal Society of Sciences and the Georg-August-Universität Göttingen. 1884: 1–13.
- .
External links
- O'Connor, John J.; Robertson, Edmund F., "Hermann Schwarz", MacTutor History of Mathematics Archive, University of St Andrews
- Hermann Schwarz at the Mathematics Genealogy Project
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