Bridge Built Between Kähler-Einstein and Chen-Ning Yang’s Equations (Maths)

Recently, Prof. CHEN Gao from Institute of Geometry and Physics of the University of Science and Technology of China has made breakthrough in the field of complex differential geometry. Using mathematical invention, he buildt a new bridge between the relativity of Einstein and quantum mechanics. This work was published in Inventiones Mathematicae.

In the field of complex differential geometry, there are two crucial physical equations: the Hermitian-Yang-Mills equation, which became the standard model of quantum mechanics, and the Kähler-Einstein equation, which is closely related to relativity. To stably solve these two equations has been at the core of complex differential geometry.

In 1977, Shing-Tung Yau solved the zero curvature Keller-Einstein equation. In 1985, Shing-tung Yau and others solved the Hermitian-Yang-Mills equation under the premise of stability. In 2012, CHEN Xiuxiong, collaborating with others, solved the positive curvature Kähler-Einstein equation under the premise of stability.

Prof. Chen’s work is another important development in this field. He solved the Chen-Donaldson’s J-equation and the supercritical deformed Hermitian-Yang-Mills equation under the premise of stability, and thus connected the Kähler-Einstein equation and the Hermitian-Yang-Mills equation.

Reviewer of Inventiones mathematicae, remarked the work as “CHEN Gao introduced two bold ideas, and solved two important equations, the results of which are very rare.” The paper has attracted the attention of the international mathematical circle and was quoted an academician of the National Academy of Sciences and others at the first time.


Reference: Chen, G. The J-equation and the supercritical deformed Hermitian–Yang–Mills equation. Invent. math. (2021). https://link.springer.com/article/10.1007%2Fs00222-021-01035-3 https://doi.org/10.1007/s00222-021-01035-3


Provided by University of Science and Technology of China

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