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Junior Analysis
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Daniel Weser, : A brief introduction to PDEs on manifolds
Friday, September 25, 2020, 03:00pm - 04:00pm
The PDE theory we learn in our classes is intimately tied to the geometry of Euclidean space. We will discuss Laplace's equation and the Poisson equation on closed hypersurfaces in R^n (primarily the sphere) to illustrate some of the ways our PDE course intuition breaks down in a curved space, even with simple equations. If time permits, I will discuss the basics of my current work with my advisor which centers around a gluing construction to produce examples of the stability of Alexandrov's theorem for compact constant mean curvature hypersurfaces.

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