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\LARGE{COURSE ANNOUNCEMENT-SPRING 1998}\\
\LARGE{Math 534-CALCULUS OF VARIATIONS}
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Depending on student interest, I plan to offer this course
with a new list of topics, emphasizing multidimensional
variational problems arising in differential geometry.
The idea is to run the course as a companion to our 500-level
PDE sequence, or for students who know some PDE and are
interested in differential geometry. The topics covered
could lead directly to a 600-level topics course containing
an introduction to areas of current research interest.
PREREQUISITE: The main prerequisite (or co-requisite)
is 535-536 (PDE). Some knowledge of differential geometry
would be helpful, but will not be assumed. Advanced calculus
and 400-level differential equations will be taken for granted.
TOPICS: Elementary Morse Theory, Morse theory of geodesics.
Existence of closed geodesics.
Minimal surfaces. First and Second variations, Jacobi operators,
stability. Solution of Plateau's problem.
Harmonic maps; the Eells-Sampson theorem
and applications. Advanced topics: the Palais-Smale condition;
unstable solutions and the mountain-pass lemma.
REFERENCES: J.Milnor, Morse Theory/
J.Jost, Differential geometry and Minimal surfaces/
H. Blaine Lawson, Lectures on minimal submanifolds/
M.Struwe, Variational Methods (advanced topics)/
INTERESTED GRADUATE STUDENTS: please indicate your interest
by e-mail to me, or leave a note in my mailbox.
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Alex Freire
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