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Hautes etudes Sci. 9892003), 105-143. ,The Zeta Functional Determinants on manifolds with boundary 1. ,The Zeta Functional Determinants on manifolds with boundary II. ,Compactification of a class of conformally flat 4-manifold, Invent. Math. 142-1(2000), 65-93. ,On the Chern-Gauss-Bonnet integral for conformal metrics on R4 , Duke Math. J. 103-3(2000),523-544. ,Extremal metrics of zeta functional determinants on 4-manifolds, ann. of Math. 142(1995), 171-212. ,On a fourth order curvature invariant.
Math. Inst. Hautes etudes Sci. 9892003), 105-143. ,The Zeta Functional Determinants on manifolds with boundary 1. ,The Zeta Functional Determinants on manifolds with boundary II. ,Compactification of a class of conformally flat 4-manifold, Invent. Math. 142-1(2000), 65-93. ,On the Chern-Gauss-Bonnet integral for conformal metrics on R4 , Duke Math. J. 103-3(2000),523-544. ,Extremal metrics of zeta functional determinants on 4-manifolds, ann. of Math. 142(1995), 171-212. ,On a fourth order curvature invariant.
To do so, we will look for zero of a operator. 2 (∂M × [0, 1]) → W m,2 (∂M × [0, 1]) as follows G(u) = Tg(t) ∂u S). − Au + (e−3u Tg0 − ∂t S i 0) Now we choose u0 such that ∂ G(u = 0 ∀ 1 ≤ i ≤ m, and u0 is bounded in L∞ (∂M × [0, 1]), in ∂ti m−1,4 m,2 W (∂M × [0, 1]), and in W (∂M × [0, 1]). We have that the Frechet derivative of G at u0 is DG(u0 )w = ∂w − Aw − 3e−3u0 w. 2 implies that the Linearization of G at u0 is bijective. Hence the Local Inversion i 0) theorem ensures that G is bijective around u0 .