José Fernando "Chepe" Escobar (born 20 December 1954, in

Manizales Manizales () is a city in central Colombia. It is the capital of the Caldas Department, Department of Caldas, and lies near the Nevado del Ruiz volcano. Currently, the city is the main center for the production of Colombian coffee and an importa ...

Colombia Colombia, officially the Republic of Colombia, is a country primarily located in South America with Insular region of Colombia, insular regions in North America. The Colombian mainland is bordered by the Caribbean Sea to the north, Venezuel ...

) was a Colombian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

known for his work on

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

and

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how ...

. He was a professor at

Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

.Cornell University News, "José Escobar, Cornell mathematics professor, dies at age 49"
/ref> He contributed to the solution of the

Yamabe problem The Yamabe problem refers to a conjecture in the mathematical field of differential geometry, which was resolved in the 1980s. It is a statement about the scalar curvature of Riemannian manifolds: By computing a formula for how the scalar curvatur ...

manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a N ...

s with boundary.

Education and career

He completed his mathematical undergraduate program at Universidad del Valle, Colombia. He received a scholarship that permitted him to do a master in science studies at the

Instituto Nacional de Matemática Pura e Aplicada The ''Instituto Nacional de Matemática Pura e Aplicada'' (National Institute for Pure and Applied Mathematics) is considered to be the foremost research and educational institution of Brazil in the area of mathematics. It is located in the cit ...

(IMPA) in Rio de Janeiro, Brazil. Escobar obtained his Ph.D. from the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

in 1986, under the supervision of

Richard Schoen Richard Melvin Schoen (born October 23, 1950) is an American mathematician known for his work in differential geometry and geometric analysis. He is best known for the resolution of the Yamabe problem in 1984 and his works on harmonic maps. Earl ...

. In his thesis he solved the problem known as the "boundary

", that had been previously settled only for the case of

s without boundary. He died from cancer on 3 January 2004, at the age 49. Mathematician Fernando Codá Marques was a Ph.D. student of him.

Recognition

Among the awards he received for his work are the Alfred P. Sloan Doctoral Dissertation Fellowship (1985-86) and the Presidential Faculty Fellowship (1992). In 2016, the

Colombian Mathematical Society The Colombian Mathematical Society (Spanish: , SCM) is an organisation founded in 1955 to promote the development of mathematics teaching and research in Colombia, and is the main professional society of Colombian mathematicians. It has two publ ...

established the ''Premio José Fernando Escobar'' for investigation in mathematics.

Selected publications

Research articles

*"The Yamabe problem on manifolds with boundary", ''

Journal of Differential Geometry The ''Journal of Differential Geometry'' is a peer-reviewed scientific journal of mathematics published by International Press on behalf of Lehigh University in 3 volumes of 3 issues each per year. The journal publishes an annual supplement in book ...

'', 1992. https://doi.org/10.4310/jdg/1214447805 *"Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary", ''

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

'', 1992. https://doi.org/10.2307/2946545 *with Richard M. Schoen: "Conformal metrics with prescribed scalar curvature", ''

Inventiones mathematicae ''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current (2023) managing ...

'', 1986. https://doi.org/10.1007/BF01389071 *"Sharp constant in a Sobolev trace inequality", '' Indiana University Mathematics Journal'', 1988. https://www.jstor.org/stable/24895334 *"Uniqueness theorems on conformal deformation of metrics, Sobolev inequalities, and an eigenvalue estimate", ''

Communications on Pure and Applied Mathematics ''Communications on Pure and Applied Mathematics'' is a monthly peer-reviewed scientific journal which is published by John Wiley & Sons on behalf of the Courant Institute of Mathematical Sciences. It covers research originating from or solicited ...

'', 1990. https://doi.org/10.1002/cpa.3160430703

Books

*''Topics in PDEs̕ and Differential Geometry'', Universidade Federal de Goiânia, 2002 E. Hebey, "Review: Topics in PDE's and differential geometry, by José F Escobar", ''

Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also pu ...

'' MR1946561 *''Some Variational Problems in Geometry'',

, 2000

References

External links

José Fernando Escobar biography at MacTutor
* L. Saloff-Coste, R. Strichartz and L. J. Billera,
José Fernando Escobar: December 20, 1954 - January 3, 2004
, ''Cornell University Faculty Memorial Statement'' 2000-2009 8 (2010), 161-163.
Obituarios: José Fernando Escobar (1954–2004) Lecturas Matemáticas, Volumen 25 (2004), páginas 127–130
1954 births 2004 deaths People from Caldas Department University of Valle alumni Cornell University faculty University of California, Berkeley alumni 21st-century Colombian mathematicians Differential geometers People from Manizales Deaths from cancer in Colombia Sloan Research Fellows 20th-century Colombian mathematicians Partial differential equation theorists Instituto Nacional de Matemática Pura e Aplicada alumni {{mathematician-stub