Shing-Tung Yau Ph.D.

National Medal of Science - Mathematics and Computer Science 1997

Mathematician. Differential geometry, Differential equations, General relativity. Calabi-Yau manifolds. Miyaoka-Yau inequality. Founder: Institute of Mathematical Sciences, Chinese University of Hong Kong; Morningside Center of Mathematics at Academia Sinica; Center of Mathematical Sciences at Zhejiang University; Tsinghua Mathematical Sciences Center, China. Adviser more than 50 doctoral students.

Family fled mainland China and Communist takeover when he was an infant. Leader of street gang and often skipped school.

Publications

1. Harmonic Functions on Complete Riemannian Manifolds, Comm. Pure Appl. Math. 28 (1975), pp. 201-228.
2. (with S. Y. Cheng) On the Regularity of the Solution of the n-Dimensional Minkowski Problem, Comm. Pure Appl. Math. 29 (1976), pp. 495-515.
3. (with Y. T. Siu) Complete Kahler manifolds with nonpositive curvature of faster than quadratic decay, Ann. of Math.(2) 105 (1977), no. 2, pp. 225-264.
4. Calabi's Conjecture and Some New Results in Algebraic Geometry, Proc. Nat. Acad. Sci. USA 74 (1977), pp.1798-1799.
5. On the Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampère Equation ?, Comm. Pure Appl. Math. 31 (1978), pp. 339-411.
6. The role of partial differential equations in differential geometry, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), pp. 237-250.
7. (With R. Schoen) Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. (2) 110 (1979), no. 1, pp. 127-142.
8. (with R. Schoen) On the Proof of the Positive Mass Conjecture in General Relativity, Comm. Math. Phys. 65 (1979), pp.45-76;?, Comm. Math. Phys. 79 (1981), pp.231-260.
9. (with Y. T. Siu) Compact Kahler Manifolds of Positive Bisectional Curvature, Invent. Math. 59 (1980), pp. 189-204.
10. (with S. Y. Cheng) On the existence of a complete Kahler metric on noncompact complex manifolds and the regularity of Fefferman's equation, Comm. Pure Appl. Math. 33 (1980), no. 4, pp. 507-544.
11. (with P. Li) Estimates of eigenvalues of a compact Riemannian manifold, Geometry of the Laplace operator, Proc. Sympos. Pure Math., XXXVI, 1980, pp. 205-239.
12. (with W. H. Meeks ?) Topology of three-dimensional manifolds and the embedding problems in minimal surface theory, Ann. of Math. (2) 112 (1980), no. 3, pp. 441-484.
13. (with P. Li) On the parabolic kernel of the Schrodinger operator, Acta Math. 156 (1986), no. 3-4, pp.153-201.
14. (with K. Uhlenbeck) On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Comm. Pure Appl. Math. 39 (1986), no. S, suppl., S257-S293.
15. (with A. Strominger and E. Zaslow) Mirror symmetry is T-duality, Nuclear Phys. B 479 (1996), no. 1-2, pp. 243--259.
16. (with B. Lian and K. Liu) Mirror principle?, Asian J. Math. 1 (1997), no. 4, pp. 729-763.
17. (with X. Gu) Computing conformal structures of surfaces. Commun. Inf. Syst. 2 (2002), no. 2, 121--145.
18. (with X. Gu and Y. Wang) Geometric compression using Riemann surface structure. Commun. Inf. Syst. 3 (2003), no. 3, 171--182 (2004).
19. (with K. Liu and X. Sun) Canonical metrics on the moduli space of Riemann surfaces. I, II. J. Diff. Geom. 68 (2004), no. 3, 571-637; 69 (2005), no. 1, 163-216.
20. (with C.C. Liu) Positivity of quasi-local mass. II. J. Amer. Math. Soc. 19 (2006), no. 1, 181--204 .
21. (with J. Fu) A Monge-Ampère-type equation motivated by string theory. Comm. Anal. Geom. 15 (2007), no. 1, 29--75.
22. (with S. S.-T. Yau) Real time solution of the nonlinear filtering problem without memory. II. SIAM J. Control Optim. 47 (2008), no. 1, 163-195.
23. (with M.-T. Wang) Isometric embeddings into the Minkowski space and new quasi-local mass, Comm. Math. Phys. 288 (2009), no. 3, 919--942.
24. (with L.-S. Tseng) Cohomology and Hodge theory on symplectic manifolds: I. J.
25. Differential Geom. 91 (2012), no. 3, 383--416; 417-443.
26. Geometry of singular space. Comm. Anal. Geom. 20 (2012), no. 5, 1097--1134.
27. (with B. H. Lian) Period integrals of CY and general type complete intersections. Invent. Math. 191 (2013), no. 1, 35--89.

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