The Yamabe problem on manifolds with boundary

A natural question in differential geometry is whether a given compact Riemannian manifold with boundary is necessarily conformally equivalent to one of constant scalar curvature, where the boundary is minimal. When the boundary is empty this is called the Yamabe Problem-so-called because, in 1960, Yamabe claimed to have solved this problem. In 1968, N. Trudinger found a mistake in Yamabe's paper In 1976, Aubin In 1984, Richard Schoen 10 solved the Yamabe problem in the remaining cases.