Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
47/1998

Mapping problems, fundamental groups and defect measures

Fanghua Lin

Abstract

We study all possible weak limits of a minimizing sequence, for p-energy functionals, consisting of continuous maps between Riemannian manifolds subject to a Dirichlet boundary condition or a homotopy condition. We show that if p is not an integer, then any such weak limit is a strong limit and, in particular, a stationary p-harmonic map which is $\mathbb{C}^{1,a}$ continuous away from a closed subset of the Hausdorff dimension $\leq n - [p] -1$. If p is an integer, then any such weak limit is a weakly p-harmonic map along with a (n-p)-rectifiable Radon measure $\mu$. Moreover, the limiting map is $\mathbb{C}^{1,a}$ continuous away from a closed subset $\Sigma =spt \mu \cup S$ with $H^{n-p} (S) = 0$. Finally, we discussed the possible varifolds type theory for Sobolev mappings.

Received:
17.11.98
Published:
17.11.98

Related publications

inJournal
1999 Repository Open Access
Fanghua Lin

Mapping problems, fundamental groups and defect measures

In: Acta Mathematica Sinica, 15 (1999) 1, pp. 25-52