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We consider the semilinear heat equation at the critical Sobolev exponent $$ u_t = \\Delta u + u^{\\frac{n+2}{n-2}} \\inn \\Omega\\times (0,\\infty), \\quad u =0 \\onn \\pp\\Omega\\times (0,\\infty). $$\n  Let $G(x,y)$ be the Dirichlet Green's function of $-\\Delta$ in $\\Omega$ and $H(x,y)$ its regular part. 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