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Perspectives on geometric analysis

by: Shing-Tung Yau
(16 Feb 2006)

X 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.

View the full article here:

arXiv (abstract), arXiv (PDF)

This article has been bookmarked 7 times, initially on 2006-02-17.

2006-11-22 User dmitri83
2006-07-13 User mnev
2006-02-22 User eibin
Group NoncommutativeGeometry
2006-02-18 User mumrah
2006-02-17 User jrw
User ansobol , 2 notes

From the introduction:

"Functions, tensors and subvarieties governed by natural differential equations provide deep insight into geometric structures. Information about these objects will give a way to construct a geometric structure. They also provide important information for physics, algebraic geometry and topology. Conversely it is vital to learn ideas from these fields.

"Behind such basic philosophy, there are basic invariants to understand how space is twisted. This is provided by Chern classes, which appear in every branch of mathematics and theoretical physics. So far we barely understand the analytic meaning of the first Chern class. It will take much more time for geometers to understand the analytic meaning of the higher Chern forms. The analytic expression of Chern classes by differential forms have opened up a new horizon for global geometry. Professor Chern’s influence on mathematics is forever."

2006-02-17 07:02:40

Reviewed by Peter Woit:

http://www.math.columbia.edu/~woit/wordpress/?p=351

2006-02-17 21:08:53
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