Perspectives on geometric analysis
Shing-Tung Yau
TL;DR
This survey reviews 30 years of developments in differential geometry, focusing on non-linear analysis, highlighting key concepts, progress, and open problems in the field.
Contribution
It provides a comprehensive overview of recent advances in geometric analysis, emphasizing the influence of non-linear methods and historical context.
Findings
Summarizes key developments in differential geometry over 30 years
Highlights the role of non-linear analysis in geometric problems
Connects historical perspectives with modern research trends
Abstract
This is a survey paper on several aspects of differential geometry for the last 30 years, especially in those areas related to non-linear analysis. It grew from a talk I gave on the occasion of seventieth anniversary of Chinese Mathematical Society. I dedicate the lecture to the memory of my teacher S.S. Chern who had passed away in December 2004.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Algebraic Geometry and Number Theory