On the Size of the Singular Set of Minimizing Harmonic Maps (Memoirs of the American Mathematical Society, 302) - Softcover

Inhaltsangabe

"We consider minimizing harmonic maps u from Rn into a closed Riemannian manifold N and prove: (1) an extension to n 4 of Almgren and Lieb's linear law. That is, if the fundamental group of the target manifold N is finite, we have (2) an extension of Hardt and Lin's stability theorem. Namely, assuming that the target manifold is we obtain that the singular set of is stable under small -perturbations of the boundary data. In dimension n = 3 both results are shown to hold with weaker hypotheses, i.e., onlyassuming that the trace of our map lies in the fractional space with and satisfying . We also discuss sharpness"-- Provided by publisher.

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