Regularity of (bi) harmonic maps
by
Alice Sun-Yung Chang
University of California at Los Angeles

Harmonic maps are critical points of the energy functional of maps between Riemannian manifolds. Existence and regularity properties of the map have been a subject of intensive study in geometric analysis. A remarkable result of Helein in 1990 establishes that any weak harmonic map defined on a surface is already smooth. The original proof of Helein replies on a compensated compactness argument of Coifman-Lions-Meyer-Semmes, which in turn is a consequence of the duality of H¹ and BMO. In this talk, I will survey results in this field, give a simpler proof of the result of Helein when the target manifold of the map is a sphere and discuss the extension of the regularity results to bi-harmonic maps.

Date received: February 1, 1999