Carl Gustav Axel Harnack
Encyclopedia
Carl Gustav Axel Harnack (May 7, 1851, Tartu
– April 3, 1888, Dresden
) was a German
mathematician
who contributed to potential theory
. Harnack's inequality
applied to harmonic function
s. He also worked on the real algebraic geometry
of plane curve
s, proving Harnack's curve theorem
for real plane algebraic curves.
He was the son of the theologian
Theodosius Harnack
and the twin brother of theologian Adolf von Harnack
(who long outlived him) - all of them from Tartu
in what is today Estonia
.
Tartu
Tartu is the second largest city of Estonia. In contrast to Estonia's political and financial capital Tallinn, Tartu is often considered the intellectual and cultural hub, especially since it is home to Estonia's oldest and most renowned university. Situated 186 km southeast of Tallinn, the...
– April 3, 1888, Dresden
Dresden
Dresden is the capital city of the Free State of Saxony in Germany. It is situated in a valley on the River Elbe, near the Czech border. The Dresden conurbation is part of the Saxon Triangle metropolitan area....
) was a German
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who contributed to potential theory
Potential theory
In mathematics and mathematical physics, potential theory may be defined as the study of harmonic functions.- Definition and comments :The term "potential theory" was coined in 19th-century physics, when it was realized that the fundamental forces of nature could be modeled using potentials which...
. Harnack's inequality
Harnack's inequality
In mathematics, Harnack's inequality is an inequality relating the values of a positive harmonic function at two points, introduced by . and generalized Harnack's inequality to solutions of elliptic or parabolic partial differential equations. Perelman's solution of the Poincaré conjecture uses...
applied to harmonic function
Harmonic function
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R which satisfies Laplace's equation, i.e....
s. He also worked on the real algebraic geometry
Real algebraic geometry
In mathematics, real algebraic geometry is the study of real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them ....
of plane curve
Plane curve
In mathematics, a plane curve is a curve in a Euclidean plane . The most frequently studied cases are smooth plane curves , and algebraic plane curves....
s, proving Harnack's curve theorem
Harnack's curve theorem
In real algebraic geometry, Harnack's curve theorem, named after Axel Harnack, describes the possible numbers of connected components that an algebraic curve can have, in terms of the degree of the curve...
for real plane algebraic curves.
He was the son of the theologian
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...
Theodosius Harnack
Theodosius Harnack
Theodosius Harnack was a Baltic German theologian.Harnack was a professor of Divinity at the University of Tartu in what is today Estonia...
and the twin brother of theologian Adolf von Harnack
Adolf von Harnack
Adolf von Harnack , was a German theologian and prominent church historian.He produced many religious publications from 1873-1912....
(who long outlived him) - all of them from Tartu
Tartu
Tartu is the second largest city of Estonia. In contrast to Estonia's political and financial capital Tallinn, Tartu is often considered the intellectual and cultural hub, especially since it is home to Estonia's oldest and most renowned university. Situated 186 km southeast of Tallinn, the...
in what is today Estonia
Estonia
Estonia , officially the Republic of Estonia , is a state in the Baltic region of Northern Europe. It is bordered to the north by the Gulf of Finland, to the west by the Baltic Sea, to the south by Latvia , and to the east by Lake Peipsi and the Russian Federation . Across the Baltic Sea lies...
.
Selected works
- Die Grundlagen der Theorie des logarithmischen Potentiales und der eindeutigen Potentialfunktion in der Ebene (Teubner, 1887)
- An introduction to the study of the elements of the differential and integral calculus Cathcart, George Lambert, tr. (Williams and Norgate, 1891)
External links
- Axel Harnack at the mathematical genealogy project
- Moritz Kassman, Harnack Inequalities: An Introduction Boundary Value Problems (2007), 81415. (An article on Harnack's inequality that contains a biography of Axel Harnack in the introduction).