The role of partial differential equations in differential geometry

Shing-Tung Yau

Differential Geometry mathscidoc:1912.43550

Proceedings of the International Congress of Mathematicians (Helsinki, 1978), 237-250, 1978
In the study of geometric objects that arise naturally, the main tools are either groups or equations. In the rst case, powerful algebraic methods are available and enable one to solve many deep problems. While algebraic methods are still important in the second case, analytic methods play a dominant role, especially when the dening equations are transcendental. Indeed, even in the situation where the geometric object is homogeneous or algebraic, analytic methods often lead to important contributions. In this talk, we shall discuss a class of problems in differential geometry and the analytic methods that are involved in solving such problems.
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@inproceedings{shing-tung1978the,
  title={The role of partial differential equations in differential geometry},
  author={Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204003471654114},
  booktitle={Proceedings of the International Congress of Mathematicians (Helsinki, 1978)},
  pages={237-250},
  year={1978},
}
Shing-Tung Yau. The role of partial differential equations in differential geometry. 1978. In Proceedings of the International Congress of Mathematicians (Helsinki, 1978). pp.237-250. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204003471654114.
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