Optimal regularity of harmonic maps from a Riemannian manifold into a static Lorentzian manifold

Takeshi Isobe

Vol. 178 (1997), No. 1, 71–93

DOI: 10.2140/pjm.1997.178.71

Abstract

In this paper, we give an optimal regularity result for some class of weakly harmonic maps from a Riemannian manifold M into a static Lorentzian manifold. Our main result is the following: For such class of weakly harmonic map w, there exists closed set Σ ⊂ M such that w is C^∞ in M ∖ Σ and the Hausdorff dimension of Σ is less than or equal to dimM − 3.

Milestones

Received: 8 June 1995

Revised: 2 October 1995

Published: 1 March 1997