Karl Hermann Amandus Schwarz was a German mathematician, born on 25 January 1843 and died on 30 November 1921. He is known for his work in complex analysis, the study of functions of a complex variable. Complex analysis is the theory of differentiable functions of a complex variable, a field where a function that is smooth once is smooth in a very strong sense, and Schwarz worked in Germany during the late nineteenth century when that theory was being developed, living from 1843 to 1921.
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Attributed Works
Source Schwarz Lantern (Wikipedia)
In Branch
Source Hermann Schwarz (Wikipedia)
Mentored By
Source Hermann Schwarz (Wikipedia)
Principal Result
Source Schwarz Lantern (Wikipedia)
Source Schwarz Lemma (Wikipedia)
Source Schwarz reflection principle (Wikipedia)
Proofs Credited
Source Schwarz Lemma (Wikipedia)
Source Schwarz reflection principle (Wikipedia)
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Source Hermann Schwarz (Wikipedia)Lead paragraph [nationality-culture]Quote, Lead paragraph [nationality-culture]
was a German mathematician
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1. Hermann Schwarz (Wikipedia)
Lead paragraph
his work in complex analysis
Lead paragraph [nationality-culture]
was a German mathematician
In Branch: Complex Analysis, Lead paragraph [in-branch]
complex analysis
- Mentored By: Karl Weierstrass, Infobox, doctoral advisor or academic advisors
View the SourceSchwarz Lemma (Wikipedia)
Wikimedia FoundationPrincipal Result: Schwarz Lemma, Lead sentence of the article on the result
In mathematics, the Schwarz lemma, named after Hermann Amandus Schwarz, is a result in complex differential geometry that estimates the (squared) pointwise norm | ∂ f | 2 {\displaystyle |\partial f|^{2}} of a holomorphic map f : ( X , g X ) → ( Y , g Y ) {\displaystyle f:(X,g_{X})\to (Y,g_{Y})} between Hermitian manifolds under curvature assumptions on g X {\displaystyle g_{X}} and g Y {\displaystyle g_{Y}} .
Proofs Credited: Schwarz Lemma, Lead paragraph
In mathematics, the Schwarz lemma, named after Hermann Amandus Schwarz, is a result in complex differential geometry that estimates the (squared) pointwise
View the Source Schwarz reflection principle (Wikipedia)
Principal Result: Schwarz Reflection Principle, Lead sentence of the article on the result
The result proved by Hermann Schwarz is as follows.
Proofs Credited: Schwarz Reflection Principle, Lead paragraph
In mathematics, the Schwarz reflection principle is a way to extend the domain of definition of a complex analytic function, i.e., it is a form of analytic
View the SourceSchwarz Lantern (Wikipedia)
Principal Result: Schwarz Lantern, Lead sentence of the article on the result
The resulting shape can be folded from paper, and is named after mathematician Hermann Schwarz and for its resemblance to a cylindrical paper lantern.
Attributed Works: Schwarz Lantern, Lead paragraph
In mathematics, the Schwarz lantern is a polyhedral approximation to a cylinder, used as a pathological example of the difficulty of defining the area
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