An Existence Theorem for the Yamabe Problem on Manifolds with Boundary Simon Brendle and Szu-yu
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چکیده
The Yamabe problem, solved by Trudinger [14], Aubin [1], and Schoen [12], asserts that any Riemannian metric on a closed manifold is conformal to a metric with constant scalar curvature. Escobar [8], [9] has studied analogous questions on manifolds with boundary. To fix notation, let (M,g) be a compact Riemannian manifold of dimension n ≥ 3 with boundary ∂M . We denote by Rg the scalar curvature of (M,g) and by κg the mean curvature of the boundary ∂M . There are two natural ways to extend the Yamabe problem to manifolds with boundary:
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تاریخ انتشار 2009