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In the case where $\Sigma$ is a Riemann sphere, the above result was obtained by Siu [S-l, $Z$] (see also [B-R-S]). In the case where $M$ is a complex projective space and deg $f|\geqq m(p-1)/(m+1)$ where $p$ denotes the genus of $\Sigma$ , the above result was obtained by Eells and Wood [E-W]. They used algebraic geometric arguments (theorems of Riemann-Roch and Grothendieck). Recently, by using a twistor space over the domain manifold, Burns and de Bartolomeis have shown the above result in the case where $M$ is a complex projective space (cf. Remark 6 of [B-R-S]). We show the above theorem by a simple argument for the second variations used in [L-S].

Stable Harmonic Maps from Riemann Surfaces to Compact Hermitian Symmetric Spaces