Nonhomogeneous expanding flows in hyperbolic spaces

Abstract In the present paper, we consider star-shaped mean convex hypersurfaces of real, complex and quaternionic hyperbolic space evolving by a class nonhomogeneous expanding flows. For any choice ambient manifold, initial conditions are preserved long-time existence flow is proved. The geometry influences asymptotic behaviour flow: after suitable rescaling, induced metric converges to conformal multiple standard Riemannian round sphere if manifold real space; otherwise, it sub-Riemannian on odd-dimensional sphere. Finally, in every case, able construct infinitely many examples such that limit does not have constant scalar curvature.