Nonuniqueness and high energy solutions for a conformally invariant scalar equation
The Yamabe problem asserts that given any compact Riemannian manifold \((M,\overline {g})\) without boundary and of dimension greater than or equal to three, there exists a conformally related metric \(g\), with constant scalar curvature. The author proves the existence of arbitrarily many distinct solutions to the Yamabe problem with constant positive scalar curvature, all lying within a fixed conformal class which is arbitrarily close, in the \(C^0\) topology, to the conformal class of any given metric of positive scalar curvature.
scientific article; zbMATH DE number 836424