Constant k-curvature hypersurfaces in Riemannian manifolds

الأصل · EN

Rugang Ye proved the existence of a family of constant mean curvature hypersurfaces in an m+1-dimensional Riemannian manifold (Mᵐ⁺¹,g), which concentrate at a point p₀ (which is required to be a nondegenerate critical point of the scalar curvature), moreover he proved that this family constitute a foliation of a neighborhood of p₀. In this paper we extend this result to the other curvatures (the r-th mean curvature for 1≤ r≤ m).