The Zero Scalar Curvature Yamabe problem on noncompact manifolds with boundary
Fernando Schwartz
53C2135J6053A3058E15Yamabe problemscalar curvaturemean curvature
Let $(M^{n},g)$, $n \ge 3$ be a noncompact complete Riemannian manifold with compact boundary and $f$ a smooth function on $\partial M$. In this paper we show that for a large class of such manifolds, there exists a metric within the conformal class of $g$ that is complete, has zero scalar curvature on $M$, and has mean curvature $f$ on the boundary. The problem is equivalent to finding a positive solution to an elliptic equation with a non-linear boundary condition with critical Sobolev exponent.
Indiana University Mathematics Journal
2006
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10.1512/iumj.2006.55.2733
10.1512/iumj.2006.55.2733
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Indiana Univ. Math. J. 55 (2006) 1449 - 1460
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