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 \begincenter{\it Math 666, Spring 1998\\

Course Information (updated) \\

Topics in Geometric Analysis on Manifolds of Non-positive Curvature }

\bigskip

\noindent
{\bf Instructor:}  

Jianguo  Cao,  221 CCMB 631-8847 (office),
                  272-4296 (home).


              



\noindent
{\bf Time to meet:}   MWF 1:55 pm - 2:45 pm  or to be re-scheduled
                      

\noindent
 {\bf Course Description:}

    This is an advanced courses in differential geometry which treats 
various topics in geometric analysis on manifolds of non-positive curvature. 

     This course will consist of two main subjects:

\noindent
(1) {\it  Analysis on manifolds of non-positive 
curvatures.}

 We will discuss the Laplace operator acting on both functions 
and forms for non-positively curved manifolds. The Dirichlet problem at infinity
will be discussed. We also discuss the non-linear equations such as  Yamabe equations and Monge-Ampere Equations.

\noindent
(2) {\it The geometric and topological structures of manifolds with non-positive 
curvature.}

 Among other things, we will discuss the Preissmann Theorem, 
Lawson-Yau and Gromoll-Wolf splitting, Eberlein-O'Neill's visibility manifolds,
and manifolds with Gromov's hyperbolicity. 



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\noindent
{\bf Pre-requirement:} None.

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\noindent
{\bf Exam:} None.

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\noindent
{\bf Homework:} Some.

 

\noindent
{\bf Reference books:} 

\begin{enumerate}
 
\item R. Schoen and S. T. Yau.: ``Lectures on Differential Geometry", 
International Press, Boston, 1994. Price:  around \$ 25.

\item P. Eberlein.: ``Geometry of Nonpositively Curved Manifolds",
The University of Chicago Press, 1996.

\item W. Ballmann, Gromov, M. and Schroeder, V.:``Manifolds of non-positive 
curvature", Birkhauser, 1985.

\end{enumerate}




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