mathematics

Peter Li (mathematician)

Peter Li (mathematician) 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 Peter Li (mathematician) rather than just read about it. In short: Peter Wai-Kwong Li (born 18 April 1952) is an American mathematician whose research interests include differential geometry and partial differential equations, with geometric analysis in particular. Mathematical work His most notable work includes the discovery of the Li–Yau differential Harnack inequalities, and the proof of the Willmore conjecture in the case of non-embedded surfaces, both done in collaboration wi…

Key takeaways

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

Reference excerpt

Peter Wai-Kwong Li (born 18 April 1952) is an American mathematician whose research interests include differential geometry and partial differential equations, with geometric analysis in particular.

Mathematical work His most notable work includes the discovery of the Li–Yau differential Harnack inequalities, and the proof of the Willmore conjecture in the case of non-embedded surfaces, both done in collaboration with Shing-Tung Yau. He is an expert on the subject of function theory on complete Riemannian manifolds.

Education and career After undergraduate work at California State University, Fresno, he earned his Ph.D. from the University of California, Berkeley, under Shiing-Shen Chern in 1979. Presently he is Professor Emeritus at University of California, Irvine, where he has been located since 1991.

Honors He has been the recipient of a Guggenheim Fellowship in 1989 and a Sloan Research Fellowship. In 2002, he was an invited speaker in the Differential Geometry section of the International Congress of Mathematicians in Beijing, where he spoke on the subject of harmonic functions on Riemannian manifolds. In 2007, he was elected a member of the American Academy of Arts and Sciences, which cited his "pioneering" achievements in geometric analysis, and in particular his paper with Yau on the differential Harnack inequalities, and its application by Richard S. Hamilton and Grigori Perelman in the proof of the Poincaré conjecture and geometrization conjecture.

Notable publications

References

External links Peter Li's website at University of California, Irvine

Worked examples

Example 1 — a first encounter with Peter Li (mathematician)

Start with the simplest possible case. Write down what Peter Li (mathematician) 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 Peter Li (mathematician) 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 Peter Li (mathematician) 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 Peter Li (mathematician)

In research: Peter Li (mathematician) 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 Peter Li (mathematician) 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: Peter Li (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1952 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Peter Li (mathematician) 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 Peter Li (mathematician) in 20 minutes

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

Frequently asked questions

What is Peter Li (mathematician) in simple terms?

Peter Wai-Kwong Li (born 18 April 1952) is an American mathematician whose research interests include differential geometry and partial differential equations, with geometric analysis in particular. Mathematical work His most notable work includes the discovery of the Li–Yau differential Harnack in…

Why does Peter Li (mathematician) 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 Peter Li (mathematician)?

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 Peter Li (mathematician).