mathematics

Paul C. Yang

Paul C. Yang 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 Paul C. Yang rather than just read about it. In short: Paul C. Yang (Chinese: 杨建平; pinyin: Yáng Jiàn Píng; born 1947) is a Taiwanese-American mathematician specializing in differential geometry, partial differential equations and CR manifolds.

Key takeaways

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

Reference excerpt

Paul C. Yang (Chinese: 杨建平; pinyin: Yáng Jiàn Píng; born 1947) is a Taiwanese-American mathematician specializing in differential geometry, partial differential equations and CR manifolds. He is best known for his work in Conformal geometry for his study of extremal metrics and his research on scalar curvature and Q-curvature. In CR Geometry he is known for his work on the CR embedding problem, the CR Paneitz operator and for introducing the Q' curvature in CR Geometry.

Career Yang received a B.A. in mathematics from the University of California, Berkeley, in 1969. He then earned his doctorate from Berkeley in 1973 under the supervision of Hung-Hsi Wu (Chinese: 伍鴻熙). He held positions at Rice University, the University of Maryland, Indiana University and the University of Southern California before joining Princeton University in 2001.

Awards and honors Yang was a Sloan Foundation Fellow in 1981. In 2012, he became a fellow of the American Mathematical Society.

Selected publications Chang, Sun-Yung A.; Yang, Paul C. Conformal deformation of metrics on S 2 {\displaystyle S^{2}} . J. Differential Geom. 27 (1988), no. 2, 259–296. Chang, Sun-Yung A.; Yang, Paul C. Prescribing Gaussian curvature on S 2 {\displaystyle S^{2}} . Acta Math. 159 (1987), no. 3–4, 215–259. Chang, Sun-Yung A.; Yang, Paul C. Extremal metrics of zeta function determinants on 4-manifolds. Ann. of Math. (2) 142 (1995), no. 1, 171–212. Chang, Sun-Yung A.; Gursky, Matthew J.; Yang, Paul C. The scalar curvature equation on 2- and 3-spheres. Calc. Var. Partial Differential Equations 1 (1993), no. 2, 205–229. Chang, Sun-Yung A.; Gursky, Matthew J.; Yang, Paul C. An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature. Ann. of Math. (2) 155 (2002), no. 3, 709–787. Yang, Paul C.; Yau, Shing-Tung Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7 (1980), no. 1, 55–63. Chanillo, Sagun; Chiu, Hung-Lin; Yang, Paul C. Embeddability for Three Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants, Duke Math. J.,161(15), (2012), 2909–2921.

References

Worked examples

Example 1 — a first encounter with Paul C. Yang

Start with the simplest possible case. Write down what Paul C. Yang 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 Paul C. Yang 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 Paul C. Yang 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 Paul C. Yang

In research: Paul C. Yang 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 Paul C. Yang 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: Paul C. Yang is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1947 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Paul C. Yang 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 Paul C. Yang in 20 minutes

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

Frequently asked questions

What is Paul C. Yang in simple terms?

Paul C. Yang (Chinese: 杨建平; pinyin: Yáng Jiàn Píng; born 1947) is a Taiwanese-American mathematician specializing in differential geometry, partial differential equations and CR manifolds.

Why does Paul C. Yang 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 Paul C. Yang?

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 Paul C. Yang.