Variational structure of $\boldsymbol{k}$-Yamabe problem on manifolds with boundary
Yan He, Sheng Weimin · Scientia Sinica Mathematica · 2017
This paper considers the $k$-Yamabe problem on manifolds with boundary. We investigate the problem under the assumption that the $k$-Yamabe equation has a variational structure instead of that the manifold is locally conformally flat, where $2\le~k 4$ with umbilic boundary if its Yamabe constant is smaller than that of the standard half unit sphere and the mean curvature of the boundary is nonnegative.