Stability of Einstein metrics on symmetric spaces of compact type

Abstract

We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces $\mathrm{SU}(n)$, $n\ge 3$, and $E_6/F_4$. Combined with earlier results, this resolves the stability problem for irreducible symmetric spaces of compact type.

v1: 19 pages. v2: 25 pages, 17 without Appendix. Added new, shorter line of proof. Added Appendix. v3: Corrected minor typos. v4: Revised version. 26 pages, 18 without Appendix