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Consider the multiple Green function $G_n$ on $E^n$: $$G_{n}(z_1,\\cdots,z_n) := \\sum_{i < j} G(z_{i} - z_{j}) - n \\sum_{i = 1} ^{n} G(z_{i}).$$ A critical point $a = (a_1, \\cdots, a_n)$ of $G_n$ is called trivial if $\\{a_1, \\cdots, a_n\\} = \\{-a_1, \\cdots, -a_n\\}$. For such a point $a$, two geometric quantities $D(a)$ and $H(a)$ arising from bubbling analysis of mean field equations are introduced. $D(a)$ is a global quantity measuring asymptotic expansion and $H(a)$ is the Hessian of $G_n$ at $a$. 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Consider the multiple Green function $G_n$ on $E^n$: $$G_{n}(z_1,\\cdots,z_n) := \\sum_{i < j} G(z_{i} - z_{j}) - n \\sum_{i = 1} ^{n} G(z_{i}).$$ A critical point $a = (a_1, \\cdots, a_n)$ of $G_n$ is called trivial if $\\{a_1, \\cdots, a_n\\} = \\{-a_1, \\cdots, -a_n\\}$. For such a point $a$, two geometric quantities $D(a)$ and $H(a)$ arising from bubbling analysis of mean field equations are introduced. $D(a)$ is a global quantity measuring asymptotic expansion and $H(a)$ is the Hessian of $G_n$ at $a$. 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