Riemannian geometry and geometric analysis

Jrgen Jost Shing-Tung Yau

Differential Geometry mathscidoc:1912.43461

42005, 2008.4
Riemannian geometry is characterized, and research is oriented towards and shaped by concepts (geodesics, connections, curvature,...) and objectives, in particular to understand certain classes of (compact) Riemannian manifolds defined by curvature conditions (constant or positive or negative curvature,...). By way of contrast, geometric analysis is a perhaps somewhat less systematic collection of techniques, for solving extremal problems naturally arising in geometry and for investigating and characterizing their solutions. It turns out that the two fields complement each other very well; geometric analysis offers tools for solving difficult problems in geometry, and Riemannian geometry stimulates progress in geometric analysis by setting ambitious goals.
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  title={Riemannian geometry and geometric analysis},
  author={Jrgen Jost, and Shing-Tung Yau},
Jrgen Jost, and Shing-Tung Yau. Riemannian geometry and geometric analysis. 2008. Vol. 42005. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203413291730025.
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