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Topology of Sobolev Mappings

Special Events

Speaker: Fengbo Hang, Princeton University
Location: 693 Kerr
Start time: Wed, Feb 4 2004, 4:10PM

We will discuss some topics related to Sobolev maps between compact Riemannian manifolds. First we will show that the [p]-1 homotopy class of a map in W^{1,p}(M,N), defined previously by White, characterizes the path connected components of W^{1,p}(M,N). This gives a clear picture of path connected components of W^{1,p}(M,N) and helps in understanding the existence of multiple solutions. Next we discuss the solution of the density problem for Sobolev maps (a question raised by Eells and Lemaire)and its relations to the existence of smooth maps in a path connected components. Finally we describe a result which identifies all the weak limits of smooth maps under the Dirichlet energy. Similar problems for higher power energy remain open.