Nonhomogeneous expanding flows in hyperbolic spaces
type: Item
instance of: scholarly article
title: Nonhomogeneous expanding flows in hyperbolic spaces
author: Giuseppe Pipoli
published in: Annals of Global Analysis and Geometry
publication date: 2022-10-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/2010.03308
review text: 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.
reviewed by: Shu-Yu Hsu
Mathematics Subject Classification ID: 53C17
Mathematics Subject Classification ID: 53E10
zbMATH DE Number: 7601376
zbMATH Keywords: curvature flows
zbMATH Keywords: hyperbolic space
zbMATH Keywords: star-shaped hypersurfaces
zbMATH Keywords: sub-Riemannian geometry
MaRDI profile type: Publication
OpenAlex ID: W3092361056
Wikidata QID: Q114227698
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DOI: 10.1007/S10455-022-09873-X
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description: scientific article; zbMATH DE number 7601376