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We show that among the metrics with a fixed value of the sum $\\beta_1+\\beta_2+\\beta_3$ and a fixed surface area, those with $\\beta_1=\\beta_2=\\beta_3$ correspond to a stationary point of the determinant. 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We show that among the metrics with a fixed value of the sum $\\beta_1+\\beta_2+\\beta_3$ and a fixed surface area, those with $\\beta_1=\\beta_2=\\beta_3$ correspond to a stationary point of the determinant. 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