The second variational formula for the functional ∫𝑣⁽⁶⁾(𝑔)𝑑𝑉_{𝑔}

Guo, Bin; Li, Haizhong

doi:10.1090/S0002-9939-2010-10703-7

The second variational formula for the functional $\int v^{(6)}(g)dV_g$
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Proc. Amer. Math. Soc. 139 (2011), 2911-2925 Request permission

Abstract:

In this paper, we compute the second variational formula for the functional $\int _M v^{(6)}(g)dv_g$, which was introduced by Graham-Juhl; the first variational formula was obtained by Chang-Fang. We also prove that an Einstein manifold (with dimension $\ge 7$) is a strict local maximum within its conformal class unless the manifold is isometric to a round sphere with the standard metric up to a multiple of a constant.

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