mathematics

José F. Escobar

José F. Escobar is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand José F. Escobar rather than just read about it. In short: José Fernando "Chepe" Escobar (born 20 December 1954, in Manizales, Colombia) was a Colombian mathematician known for his work on differential geometry and partial differential equations. He was a professor at Cornell University.

Key takeaways

José F. Escobar belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect José F. Escobar to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of José F. Escobar from memory before moving on to harder problems.

Reference excerpt

José Fernando "Chepe" Escobar (born 20 December 1954, in Manizales, Colombia) was a Colombian mathematician known for his work on differential geometry and partial differential equations. He was a professor at Cornell University. He contributed to the solution of the Yamabe problem on manifolds 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 (IMPA) in Rio de Janeiro, Brazil. Escobar obtained his Ph.D. from the University of California, Berkeley in 1986, under the supervision of Richard Schoen. In his thesis he solved the problem known as the "boundary Yamabe problem", that had been previously settled only for the case of manifolds without boundary. He died from cancer on 3 January 2004, at the age 49. Mathematician Fernando Codá Marques was a Ph.D. student of his.

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 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, 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, 1992. https://doi.org/10.2307/2946545 with Richard M. Schoen: "Conformal metrics with prescribed scalar curvature", Inventiones mathematicae, 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, 1990. https://doi.org/10.1002/cpa.3160430703

Books Topics in PDEs̕ and Differential Geometry, Universidade Federal de Goiânia, 2002 Some Variational Problems in Geometry, Instituto Nacional de Matemática Pura e Aplicada, 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

Worked examples

Example 1 — a first encounter with José F. Escobar

Start with the simplest possible case. Write down what José F. Escobar claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to José F. Escobar before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about José F. Escobar ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of José F. Escobar

In research: José F. Escobar appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses José F. Escobar in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: José F. Escobar is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1954 births, 2004 deaths, 20th-century Colombian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for José F. Escobar outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study José F. Escobar in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what José F. Escobar means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain José F. Escobar out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is José F. Escobar in simple terms?

Why does José F. Escobar matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study José F. Escobar?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on José F. Escobar.