Knowra Shing-Tung Yau Shing-Tung Yau Shing-Tung Yau is a Chinese-born American mathematician whose work in differential geometry includes proving the Calabi conjecture and the positive mass theorem.
Calabi conjecture : A conjecture that compact Kähler manifolds admit a unique metric with prescribed volume form within a fixed Kähler class. Yau’s 1976 proof established the existence of Ricci-flat Kähler metrics central to complex geometry.
Complex Monge–Ampère equation : A nonlinear partial differential equation involving the determinant of the complex Hessian of a function. Yau solved this equation to prove the Calabi conjecture.
Eugenio Calabi : An Italian-American mathematician who formulated the conjecture later proved by Yau. Calabi posed the geometric existence problem that became one of Yau’s best-known achievements.
Chinese University of Hong Kong : A public research university in Hong Kong, founded in 1963. Yau studied mathematics there before moving to the United States for graduate study.
Uniformization theorem : A theorem classifying simply connected Riemann surfaces as the sphere, complex plane, or unit disk. Unlike Yau’s higher-dimensional existence theorem, uniformization classifies complex curves through their universal covers.
Calabi–Yau manifold : A compact Kähler manifold with vanishing first Chern class, equipped in many applications with a Ricci-flat metric. Yau’s theorem supplies the Ricci-flat metrics that give these manifolds their defining geometric structure.
Kähler geometry : The study of complex manifolds equipped with a compatible Hermitian metric whose associated two-form is closed. The Calabi conjecture is formulated within this geometric setting.
Richard Schoen : An American mathematician whose work spans differential geometry, geometric analysis, and partial differential equations. Schoen collaborated with Yau on the positive mass theorem and other geometric problems.
University of California, Berkeley : A public research university in Berkeley, California, established in 1868. Yau completed his doctoral studies in mathematics at Berkeley under Shiing-Shen Chern.
Positive energy theorem : A result in general relativity asserting nonnegative total energy for suitable asymptotically flat initial data. This broader name is often used for the result whose mathematical proof Yau and Schoen established.
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