Nonhomogeneous expanding flows in hyperbolic spaces
The author studies star-shaped mean convex hypersurfaces of the real, complex and quaternionic hyperbolic type evolving by a class of nonhomogeneous expanding flows. Among other results, he proves the global existence of a solution of the flow which preserves the initial conditions. He also shows that after a suitable rescaling the induced metric converges to a conformal multiple of the standard metric of the sphere when the ambient manifold is the real hyperbolic space and it converges to a conformal multiple of the standard sub-Riemannian metric on odd-dimensional sphere in the other cases. Examples such that the limit does not have constant scalar curvature are presented.
scientific article; zbMATH DE number 7601376
scientific article