Math 642: Topics in Partial Differential Equations |
Fall 2015 |
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Faculty: Jerry L. KazdanTelephone: (215) 898-5109

email:kazdan AT math.upenn.eduOffice Hours: by appointment in DRL 4E15

Topics:Prerequisites: Math 608, 609. [This course will not presume courses in Partial Differential Equations or Differential Geometry. Background will be covered in the course.] Problems in differential geometry, as well as those in physics and engineering, inevitable involve partial derivatives. This course will be an introduction to these problems and techniques. We will use PDE as a tool, carefully explaining the needed background -- but not proving the details. Some of the applications will be "small," some "large". The proof of the Hodge Theorem will be a small application. Discussion of the Yamabe problem and Ricci flow (used to prove the Poincare Conjecture) will be larger.Some References

Solving -Δu=h(x)e^{u}[see pages 27-28]

Ricci-DeTurck Flow

Osserman, Robert,A Survey of Minimal Surfaces, Dover Publications, 1986.

Meeks, W. and Perez, J.A survey on classical minimal surface theory2008?

Some Homework ProblemsStudents registered for the course should do at least 4 homework problems this semester. To give you further selection I will be adding to this collection of problems.