Reprinted from Yau's 1986 monograph in L'Enseignement Mathématique, this chapter surveys the interplay between eigenvalues, harmonic functions, and PDEs. explores connections between spectral geometry and potential theory. §2. Yamabe's Equation and Conformally Flat Manifolds revisits the Yamabe problem in the broader context of nonlinear elliptic equations. §3. Harmonic Maps surveys the theory of maps between manifolds that minimize the Dirichlet energy—a subject of immense importance to which both authors have made lasting contributions.
The lectures on differential geometry by Richard Schoen and Shing-Tung Yau are a renowned series of lectures that have been widely circulated in the mathematics community. The lectures were delivered by Schoen and Yau, two prominent mathematicians in the field of differential geometry, at various institutions.
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The unique value of the lecture format is the inclusion of "back-of-the-envelope" calculations, open problems (as of the 1990s), and intuitive insights that rarely make it into polished textbooks.
What is "Lectures on Differential Geometry" by Schoen and Yau? The lectures on differential geometry by Richard Schoen
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If you're interested in learning differential geometry, I recommend checking out the following books: Share public link
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