Paul C. Yang (; born 1947) is a

Taiwanese-American Taiwanese Americans ( Chinese: 臺灣裔美國人; pinyin: ''Táiwān yì měiguó rén''; Pe̍h-ōe-jī: ''Tâi-Bí-jîn'') are Americans of Taiwanese ancestry, including American-born descendants of migrants from the Republic of China (Taiwan) ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

specializing in

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s and

CR manifold In mathematics, a CR manifold, or Cauchy–Riemann manifold, is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge. Forma ...

s. He is best known for his work in Conformal geometry for his study of extremal metrics and his research on

scalar curvature In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry ...

and Q-curvature. In CR Geometry he is known for his work on the CR embedding problem, the CR

Paneitz operator In the mathematics, mathematical field of differential geometry, the Paneitz operator is a fourth-order differential operator defined on a Riemannian manifold of dimension ''n''. It is named after Stephen Paneitz, who discovered it in 1983, and who ...

and for introducing the Q' curvature in CR Geometry.

Career

Yang received a

B.A. A Bachelor of Arts (abbreviated B.A., BA, A.B. or AB; from the Latin ', ', or ') is the holder of a bachelor's degree awarded for an undergraduate program in the liberal arts, or, in some cases, other disciplines. A Bachelor of Arts degree ...

in mathematics from the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, in 1969. He then earned his doctorate from Berkeley in 1973 under the supervision of Hung-Hsi Wu (). He held positions at

Rice University William Marsh Rice University, commonly referred to as Rice University, is a Private university, private research university in Houston, Houston, Texas, United States. Established in 1912, the university spans 300 acres. Rice University comp ...

, the

University of Maryland The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD is the flagship institution of the Univ ...

Indiana University Indiana University (IU) is a state university system, system of Public university, public universities in the U.S. state of Indiana. The system has two core campuses, five regional campuses, and two regional centers under the administration o ...

and the

University of Southern California The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in ...

before joining

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

in 2001.

Awards and honors

Yang was a

Sloan Foundation The Alfred P. Sloan Foundation is an American philanthropic nonprofit organization. It was established in 1934 by Alfred P. Sloan Jr., president and chief executive officer of General Motors. The Sloan Foundation makes grants to support origin ...

Fellow in 1981. In 2012, he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

.List of Fellows of the American Mathematical Society
/ref>

Selected publications

*Chang, Sun-Yung A.; Yang, Paul C. ''Conformal deformation of metrics on

S^2

''. J. Differential Geom. 27 (1988), no. 2, 259–296. *Chang, Sun-Yung A.; Yang, Paul C. ''Prescribing Gaussian curvature on

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 surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

s 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

{{DEFAULTSORT:Yang, Paul C. Living people 20th-century American mathematicians 21st-century American mathematicians Fellows of the American Mathematical Society University of California, Berkeley alumni Rice University faculty University of Maryland, College Park faculty Indiana University faculty University of Southern California faculty Princeton University faculty American people of Chinese descent Differential geometers Chinese mathematicians 1947 births People from Changhua County