On the asymptotic behavior of expanding gradient Ricci solitons
type: Item
instance of: scholarly article
title: On the asymptotic behavior of expanding gradient Ricci solitons
zbMATH Open document ID: 1263.53061
author: Chih-Wei Chen
published in: Annals of Global Analysis and Geometry
publication date: 2012-11-21T00:00:00Z
review text: Consider an \(n\)-dimensional expanding gradient Ricci soliton \((M,g,f)\) with faster-than-quadratic-decay of curvature, that is, \[ \lim_{\text{dist} (O,x)\rightarrow \infty} |\mathrm{Sect}(x)|\cdot \mathrm{dist}(O,x)^2=0. \] The main result of this paper shows that if \(M\) is simply connected at infinity and \(n\geq 3\), then its tangent cone at infinity must be a manifold isometric to \(\mathbb R^n\).
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 6109315
zbMATH Keywords: Ricci flow
zbMATH Keywords: Expanding solutions
zbMATH Keywords: curvature decay
MaRDI profile type: Publication
full work available at URL: s10455-012-9311-7
OpenAlex ID: W2024135928
cites work: On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth
cites work: Limits of solutions to the Kähler-Ricci flow
cites work: On complete gradient shrinking Ricci solitons
cites work: Q3597021
cites work: Sharp logarithmic Sobolev inequalities on gradient solitons and applications
cites work: The evolution of the Weyl tensor under the Ricci flow
cites work: Lower bounds on Ricci curvature and the almost rigidity of warped products
cites work: Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
cites work: Strong uniqueness of the Ricci flow
cites work: Complete Riemannian manifolds with pointwise pinched curvature
cites work: On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold
cites work: Q3413423
cites work: A necessary and sufficient condition for Ricci shrinkers to have positive AVR
cites work: Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons
cites work: Spacetime energy decreases under world-sheet RG flow
cites work: The Harnack estimate for the Ricci flow
cites work: Q4873981
cites work: Noncompact shrinking four solitons with nonnegative curvature
cites work: Ancient solutions to Kähler-Ricci flow
cites work: On a classification of gradient shrinking solitons
cites work: Q5485637
cites work: On the classification of gradient Ricci solitons
cites work: Complete shrinking Ricci solitons have finite fundamental group
cites work: Gradient shrinking solitons with vanishing Weyl tensor
cites work: On the completeness of gradient Ricci solitons
cites work: On a sharp volume estimate for gradient Ricci solitons with scalar curvature bounded below
Wikidata QID: Q125976848
DOI: 10.1007/S10455-012-9311-7
description: scientific article; zbMATH DE number 6109315