The Q-curvature on a 4-dimensional Riemannian Manifold
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چکیده
One of the most important problem in conformal geometry is the construction of conformal metrics for which a certain curvature quantity equals a prescribed function, e.g. a constant. In two dimensions, the problem of prescribed Gaussian curvature asks the following: given a smooth function K on (M,g0), can we find a metric g conformal to g0 such that K is the Gaussian curvature of the new metric g? If let g = eg0 for some u ∈ C∞(M), then the problem is equivalent to solving the nonlinear elliptic equation: ∆u+Ke −K0 = 0, (1.1)
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تاریخ انتشار 2006