论文标题
具有边界上的Yamabe类型方程的等距函数和解决方案
Isoparametric functions and solutions of Yamabe type equations on manifolds with boundary
论文作者
论文摘要
令$（m，g）$为具有非空边界的紧凑型Riemannian歧管。提供$ f $ a $（m，g）$的等载函数，我们证明了yamabe方程的积极解决方案的存在结果，这些解决方案沿$ f $的级别持续。如果$（m，g）$具有正常的标量曲率，最小的边界，并承认等于Yamabe方程的正溶液在$（m \ times n，g+th）上，我们也证明了多重结果，其中$（n，h）$是任何封闭的Riemannian sparter scalar scalar curvature sustance nose coble。
Let $(M,g)$ be a compact Riemannian manifold with non-empty boundary. Provided $f$ an isoparametric function of $(M,g)$ we prove existence results for positive solutions of the Yamabe equation that are constant along the level sets of $f$. If $(M,g)$ has positive constant scalar curvature, minimal boundary and admits an isoparametric function we also prove multiplicity results for positive solutions of the Yamabe equation on $(M \times N,g+th) $ where $(N,h)$ is any closed Riemannian manifold with positive constant scalar curvature.
