mathematics

Pierre Lelong

Pierre Lelong 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 Pierre Lelong rather than just read about it. In short: Pierre Lelong (14 March 1912 Paris – 12 October 2011) was a French mathematician who introduced the Poincaré–Lelong equation, the Lelong number and the concept of plurisubharmonic functions. Career Lelong earned his doctorate in 1941 from the École Normale Supérieure, under the supervision of Paul Montel.

Key takeaways

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

Reference excerpt

Pierre Lelong (14 March 1912 Paris – 12 October 2011) was a French mathematician who introduced the Poincaré–Lelong equation, the Lelong number and the concept of plurisubharmonic functions.

Career Lelong earned his doctorate in 1941 from the École Normale Supérieure, under the supervision of Paul Montel. On 5 June 1981 Lelong received an honorary doctorate from the Faculty of Mathematics and Science at Uppsala University, Sweden. He became a member of the French Academy of Sciences in 1985.

Lelong has made many pioneering contributions in mathematics. Especially of great impact is his work on the Poincaré-Lelong equation, closed positive currents and Lelong numbers. The best way to understand this very important part of his work is to look at it from the historic perspective of constructing meromorphic functions on abstractly defined complex manifolds and see how his contributions fit in a pivotal way into the global landscape in the theory of several complex variables.The theory of several complex variables studies complex-analytic objects such as holomorphic and meromorphic functions and maps, complex-analytic subvarieties, holomorphic vector bundles, and coherent analytic sheaves. When a complex-analytic manifold or space is projective algebraic, by definition it is embedded inside a complex projective space and there are many complex- analytic objects on it which are constructed from those on the complex projective space. When a complex-analytic manifold is abstractly defined by piecing together local holomorphic charts, the construction of complex-analytic objects on it is a problem of fundamental importance.

Personal life He married another mathematician, Jacqueline Ferrand, in 1947; they separated in 1977.

References

Illustrations

Worked examples

Example 1 — a first encounter with Pierre Lelong

Start with the simplest possible case. Write down what Pierre Lelong 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 Pierre Lelong 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 Pierre Lelong 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 Pierre Lelong

In research: Pierre Lelong 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 Pierre Lelong 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: Pierre Lelong is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1912 births, 2011 deaths, 20th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Pierre Lelong 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 Pierre Lelong in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Pierre Lelong 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 Pierre Lelong out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Pierre Lelong in simple terms?

Pierre Lelong (14 March 1912 Paris – 12 October 2011) was a French mathematician who introduced the Poincaré–Lelong equation, the Lelong number and the concept of plurisubharmonic functions. Career Lelong earned his doctorate in 1941 from the École Normale Supérieure, under the supervision of Paul…

Why does Pierre Lelong 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 Pierre Lelong?

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 Pierre Lelong.