At first glance, it appears to be a simple request for a file. But for graduate students, postdocs, and research mathematicians, this string of words represents a holy grail. It combines two towering figures in 20th-century geometry—Richard Schoen and Shing-Tung Yau—with a specific pedagogical format (lectures) and the urgent desire for a " new " version.
If you wish to conduct the search yourself, here is a professional strategy:
Lectures on Differential Geometry by Richard Schoen and Shing-Tung Yau is a seminal work in the field of geometric analysis, originating from a series of lectures delivered at the Institute for Advanced Study
Geometric analysis on complete, non-compact manifolds. schoen yau lectures on differential geometry pdf new
: Modern re-issues and related graduate catalogs are indexed comprehensively on the American Mathematical Society (AMS) Bookstore platform, which provides digital chapter breakdowns.
(Stanford) and Shing-Tung Yau (Harvard, now Tsinghua) are titans of differential geometry. In the late 1970s and early 1980s, they revolutionized the field of geometric analysis. Their most famous collaboration was the solution to the Yamabe Problem , but their most profound legacy for the lectures is their work on minimal surfaces and positive mass theorem .
One of the most famous features of the book is its extensive lists of open problems (nearly 220 in total). These provide a roadmap for the research programme of using curvature to understand topology. At first glance, it appears to be a
I understand you're looking for information on a PDF of lectures on differential geometry by and Shing-Tung Yau , likely based on their classic graduate-level course or notes.
The landmark text by legendary mathematicians Richard Schoen and Shing-Tung Yau stands as one of the most influential foundations for modern geometric analysis. Originating from a historic lecture series delivered at the Institute for Advanced Study (IAS) in Princeton, this work bridged classical Riemannian geometry with partial differential equations (PDEs), transforming how physicists and mathematicians analyze curved spaces. Finding high-quality, newly accessible digital versions or official PDFs of this seminal volume is essential for advanced students, researchers, and mathematical physicists trying to master the techniques that solved the Positive Mass Conjecture and the Yamabe problem. The Legacy of the Schoen-Yau Lectures Historical Context
The influence of this book extends far beyond its pages. The concepts and techniques Schoen and Yau developed have continued to stimulate groundbreaking research. In 2024 and 2025, for instance, new papers were published extending the to prove scalar-mean rigidity theorems for manifolds with boundary. Other recent work has used their framework to investigate topological obstructions to positive scalar curvature on open manifolds. If you wish to conduct the search yourself,
And then, perhaps, you will be the one to compile and typeset the truly new Schoen-Yau lectures for the next generation.
One of the book’s most valuable features is its extensive lists of in differential geometry, curated by the authors to guide future research. Editions and Availability