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From Wikipedia, the free encyclopedia

Paul C. Yang
Known forDifferential geometry
Partial differential equations
SpouseSun-Yung Alice Chang
Awards
Scientific career
FieldsMathematics
InstitutionsRice University
University of Maryland
Indiana University
University of Southern California
Princeton University
Doctoral advisorHung-Hsi Wu

Paul C. Yang (Chinese: 杨建平; pinyin: Yáng Jiàn Píng; Wade–Giles: Chien-Ping Yang ,1947 in Changhua, Taiwan) 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.

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  • The hidden meanings of yin and yang - John Bellaimey

Transcription

You might have seen this symbol before, whether it's as a temporary tattoo or at a Chinese temple. It's called the yin-yang symbol. It comes from Taoism, a religion born in China and it has far more meaning than you probably realize. The yin is the dark swirl, and the yang is the light one, and each side has a dot of the opposite color, which gives a clue to the meaning of yin and yang. Everything contains the seed of its opposite. Darth Vadar has the seed of goodness, and Luke has the potential to follow his father to the dark side. Like Luke and his father, yin and yang are not total opposites, they are relative to each other. Taoists believe that the universe is made up of energies, vibrations, and matter, which behave differently in different contexts. Something can be yin or yang depending on, well, depending on lots of things. So, while wheat that's growing is yang, when it's being reaped, it's yin. A wave's crest is yang, and the trough is yin. Villages on the sunny side of a valley in China have names like Liuyang or Shiyang, but on the shady side, for example, of the Yangtze River Valley, there's Jiangyin. The brake is yin to the gas pedal's yang. An eggshell is yang, the egg inside is yin. You think you're getting it? Yang is harder, stronger, brighter, and faster, but one can turn into the other or are two sides of the same coin. The sunbeams are yang in comparison to the shadows. The pitch is yang, the catch is yin. The yang starts an action, and the yin receives it, completes it. Yin is the inside space of a cup; it wouldn't be a cup without it. Yang is the cup. The coffee's heat, however, is yang, and its blackness is yin. Yang goes berserk sometimes, but there's some very powerful yins, too, if they don't quite go berserk. Yin is the darker swirl, the female, but there is a white dot in it. And yang is the lighter, the male, but it has a black dot. Water flowing calmly in a river is yin, but when it goes over the waterfall, it's very yang. Toothpicks are yin compared with a telephone pole. The back of a person is more yin than the front. The top of a person is the yang end. Taoism teaches that there is a power in the universe. It's higher, deeper, and truer than any other force. They call it the Tao. It means the way. Like the Force in Star Wars, the Tao has two sides. Unlike other religions where the higher power is all good, and perhaps has an all-evil rival, Taoism teaches that we need to learn from both yin and yang. And unlike religions with gods that are personal, the higher power in Taoism is not. Taoists believe that living in harmony with the way, a person will not have to fight against the universe's natural flow. So, for example, listen more, argue less. Be ready to back up or undo something, and you will make even faster progress. Don't worry about being the best, be who you are. Live simply. Complications take you away from the Tao. "The wise person is flexible," Taoists say. Learning to use the Tao is what Taoism is all about, and that's why you should know your yin from your yang.

Career

Yang earned his doctorate at the University of California, Berkeley in 1973 under the supervision of Hung-Hsi Wu(Chinese: 伍鴻熙).[1] He held positions at Rice University, the University of Maryland, Indiana University and the University of Southern California before joining Princeton University in 2001.[2]

Awards and honors

Yang was a Sloan Foundation Fellow in 1981.[2] In 2012, he became a fellow of the American Mathematical Society.[3]

Selected publications

  • Chang, Sun-Yung A.; Yang, Paul C. Conformal deformation of metrics on . J. Differential Geom. 27 (1988), no. 2, 259–296.
  • Chang, Sun-Yung A.; Yang, Paul C. Prescribing Gaussian curvature on . 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

  1. ^ Paul Yang at the Mathematics Genealogy Project
  2. ^ a b "Princeton:Professor Yang". Retrieved Mar 10, 2015.
  3. ^ List of Fellows of the American Mathematical Society
This page was last edited on 7 September 2023, at 14:36
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