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Shing-Tung Yau
Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician. He is the director of the Yau Mathematical Sciences Center at Tsinghua University and professor emeritus at Harvard University. Until 2022, Yau was the William Caspar Graustein Professor of Mathematics at Harvard, at which point he moved to Tsinghua. Yau was born in Shantou in 1949, moved to British Hong Kong at a young age, and then moved to the United States in 1969. He was awarded the Fields Medal in 1982, in recognition of his contributions to partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors to the development of modern differential geometry and geometric analysis. The impact of Yau's work are also seen in the mathematical and physical fields of convex geometry, algebraic geometry, enumerative geometry, mirror symmetry, general relativity, and string theory, while his work h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Shing-Toung Yau
Stephen Shing-Toung Yau (; born 1952) is a Chinese-American mathematician. He is a Distinguished Professor Emeritus at the University of Illinois at Chicago, and currently teaches at Tsinghua University. He is a Fellow of the Institute of Electrical and Electronics Engineers and the American Mathematical Society. Biography Shing-Toung Yau was born in 1952 in British Hong Kong, with his Ancestral home (Chinese), ancestral home in Jiaoling County, Guangdong, China. He is the younger brother of Fields Medalist Shing-Tung Yau. After graduating from the Chinese University of Hong Kong, he studied mathematics at the State University of New York at Stony Brook, where he learnt after Henry Laufer and earned his M.A. in 1974 and Ph.D. in 1976. He was a member of the Institute for Advanced Study at Princeton, New Jersey, Princeton from 1976 to 1977 and from 1981 to 1982, and was a Benjamin Pierce Assistant Professor at Harvard University from 1977 to 1980. He subsequently taught at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Huai-Dong Cao
Huai-Dong Cao (born 8 November 1959, in Jiangsu) is a Chinese-born American mathematician. He is the A. Everett Pitcher Professor of Mathematics at Lehigh University. He is known for his research contributions to the Ricci flow, a topic in the field of geometric analysis. Academic history Cao received his B.A. from Tsinghua University in 1981 and his Ph.D. from Princeton University in 1986 under the supervision of Shing-Tung Yau. Cao is a former Associate Director, Institute for Pure and Applied Mathematics (IPAM) at UCLA. He has held visiting Professorships at MIT, Harvard University, Isaac Newton Institute, Max-Planck Institute, IHES, ETH Zurich, and University of Pisa. He has been the managing editor of the ''Journal of Differential Geometry'' since 2003. His awards and honors include: * Sloan Research Fellowship (1991-1993) * Guggenheim Fellowship (2004) * Outstanding Overseas Young Researcher Award awarded by the National Natural Science Foundation of China (2005) Mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bogomolov–Miyaoka–Yau Inequality
In mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality : c_1^2 \le 3 c_2 between Chern numbers of compact complex surfaces of general type. Its major interest is the way it restricts the possible topological types of the underlying real 4-manifold. It was proved independently by and , after and proved weaker versions with the constant 3 replaced by 8 and 4. Armand Borel and Friedrich Hirzebruch showed that the inequality is best possible by finding infinitely many cases where equality holds. The inequality is false in positive characteristic: and gave examples of surfaces in characteristic ''p'', such as generalized Raynaud surfaces, for which it fails. Formulation of the inequality The conventional formulation of the Bogomolov–Miyaoka–Yau inequality is as follows. Let ''X'' be a compact complex surface of general type, and let ''c''1 = ''c''1(''X'') and ''c''2 = ''c''2(''X'') be the first and second Chern class of the complex tangent bundl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximal Surface
In the mathematical field of differential geometry, a maximal surface is a certain kind of submanifold of a Lorentzian manifold. Precisely, given a Lorentzian manifold , a maximal surface is a spacelike submanifold of whose mean curvature is zero. As such, maximal surfaces in Lorentzian geometry are directly analogous to minimal surfaces in Riemannian geometry. The difference in terminology between the two settings has to do with the fact that small regions in maximal surfaces are local maximizers of the area functional, while small regions in minimal surfaces are local minimizers of the area functional. In 1976, Shiu-Yuen Cheng and Shing-Tung Yau resolved the "Bernstein problem" for maximal hypersurfaces of Minkowski space which are properly embedded, showing that any such hypersurface is a plane. This was part of the body of work for which Yau was awarded the Fields medal in 1982. The Bernstein problem was originally posed by Eugenio Calabi in 1970, who proved some special cases o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernstein's Problem
In differential geometry, Bernstein's problem is as follows: if the graph of a function on R''n''−1 is a minimal surface in R''n'', does this imply that the function is linear? This is true for ''n'' at most 8, but false for ''n'' at least 9. The problem is named for Sergei Natanovich Bernstein who solved the case ''n'' = 3 in 1914. Statement Suppose that ''f'' is a function of ''n'' − 1 real variables. The graph of ''f'' is a surface in R''n'', and the condition that this is a minimal surface is that ''f'' satisfies the minimal surface equation :\sum_^ \frac\frac = 0 Bernstein's problem asks whether an ''entire'' function (a function defined throughout R''n''−1 ) that solves this equation is necessarily a degree-1 polynomial. History proved Bernstein's theorem that a graph of a real function on R2 that is also a minimal surface in R3 must be a plane. gave a new proof of Bernstein's theorem by deducing it from the fact that t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimal Surface
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However, the term is used for more general surfaces that may self-intersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see minimal surface of revolution): the standard definitions only relate to a local optimum, not a global optimum. Definitions Minimal surfaces can be defined in several equivalent ways in \R^3. The fact that they are equivalent serves to demonstrate how minimal surface theory lies at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plateau Problem
In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760. However, it is named after Joseph Plateau who experimented with soap films. The problem is considered part of the calculus of variations. The existence and regularity problems are part of geometric measure theory. History Various specialized forms of the problem were solved, but it was only in 1930 that general solutions were found in the context of mappings (immersions) independently by Jesse Douglas and Tibor Radó. Their methods were quite different; Radó's work built on the previous work of René Garnier and held only for rectifiable curve, rectifiable simple closed curves, whereas Douglas used completely new ideas with his result holding for an arbitrary simple closed curve. Both relied on setting up minimization problems; Douglas minimized the now-named Douglas integral while Radó minimized the "energy". Douglas went ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Valentino Tosatti
Valentino Tosatti (born ) is an Italian mathematician. Biography Born , in Trieste, Tosatti studied from 2000 at the Scuola Normale Superiore di Pisa and at the University of Pisa, graduating with a ''laurea'' in 2004. He then studied at Harvard University, where he graduated with an M.A. in 2005 and a Ph.D. in 2009. (CV has comprehensive publication list.) His Ph.D. thesis ''Geometry of complex Monge-Ampère equations'' was supervised by Shing-Tung Yau. Tosatti was from 2009 to 2012 a Joseph Fels Ritt Assistant Professor at Columbia University. At Northwestern University, he was an associate professor from 2012 to 2015 and a full professor from 2015 to 2020. From 2020 to 2022, he taught as a professor at McGill University. In 2022 he became a professor at NYU's Courant Institute of Mathematical Sciences. Tosatti does research on complex and differential geometry; geometric analysis on complex, Hermitian, and symplectic manifolds; and partial differential equations. He is also i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiu-Chu Melissa Liu
Chiu-Chu Melissa Liu (; born 15 December 1974) is a Taiwanese mathematician who works as a professor of mathematics at Columbia University. Her research interests include algebraic geometry and symplectic geometry.Curriculum vitae , retrieved 2015-01-12. Early life and education Liu was born on December 16, 1974, in Taiwan. She graduated from with her (B.S.) in mathematics in 1996 and earned her Ph.D. from |
Mu-Tao Wang
Mu-Tao Wang () is a Taiwanese mathematician who is a professor of mathematics at Columbia University. Education In 1984, Wang enrolled in National Taiwan University (NTU) with the initial intent to study international business but, after a year, he switched to mathematics. He graduated from NTU with his Bachelor of Science (B.S.) in 1988 and his Master of Science (M.S.) in 1992, both in mathematics. Wang then completed advanced studies in the United States, where he earned his Ph.D. in mathematics in 1998 from Harvard University. His doctoral dissertation was titled, "Generalized harmonic maps and representations of discrete groups," was by supervised by Fields Medalist laureate Shing-Tung Yau. Career Wang joined the Columbia faculty as an assistant professor in 2001, and was appointed full professor in 2009. Before joining the faculty at Columbia, Wang was Szego Assistant Professor at Stanford University. He was a Sloan Research Fellow from 2003 to 2005. In 2007, he was named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kefeng Liu
Kefeng Liu (; born 12 December 1965), is a Chinese-American mathematician who is known for his contributions to geometric analysis, particularly the geometry, topology and analysis of moduli spaces of Riemann surfaces and Calabi–Yau manifolds. He is a professor of mathematics at University of California, Los Angeles, as well as the executive director of the Center of Mathematical Sciences at Zhejiang University. He is best known for his collaboration with Bong Lian and Shing-Tung Yau in which they establish some enumerative geometry conjectures motivated by mirror symmetry. Biography Liu was born in Kaifeng, Henan province, China. In 1985, Liu received his B.A. in mathematics from the Department of Mathematics of Peking University in Beijing. In 1988, Liu obtained his M.A. from the Institute of Mathematics of the Chinese Academy of Sciences (CAS) in Beijing. Liu then went to study in the United States, obtaining a Ph.D. from Harvard University in 1993 under Shing-Tung Yau. F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lizhen Ji
Lizhen Ji (Chinese: 季理真; born 1964), is a Chinese American mathematician. He is a professor of mathematics at the University of Michigan. Biography In 1964, Ji was born in Wenzhou, Zhejiang Province, China. Ji graduated with a B.S. from Hangzhou University (now Zhejiang University) in Hangzhou in 1984. From 1984 to 1985, Ji was a master student at the Department of Mathematics of Hangzhou University. Ji went to United States to continue his study in 1985, and in 1987 Ji obtained a M.S. from the Department of Mathematics of the University of California, San Diego. In 1991, Ji obtained a Ph.D. from the Northeastern University. His thesis ''Spectral Degeneration of Riemann Surfaces'' was advised by R. Mark Goresky and Shing-Tung Yau. From 1991 to 1994, Ji was C.L.E. Moore instructor at the Department of Mathematics of MIT. From 1994 to 1995, Ji was a member of the Institute for Advanced Study School of Mathematics in Princeton, New Jersey. From 1995 to 1999, Ji was an assi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
