Open Access
Translator Disclaimer
May 2015 Rigidity of asymptotically conical shrinking gradient Ricci solitons
Brett Kotschwar, Lu Wang
J. Differential Geom. 100(1): 55-108 (May 2015). DOI: 10.4310/jdg/1427202764


We show that if two gradient shrinking Ricci solitons are asymptotic along some end of each to the same regular cone $((0,\infty) \times \Sigma, dr^2 + r^2 g_{\Sigma} )$, then the soliton metrics must be isometric on some neighborhoods of infinity of these ends. Our theorem imposes no restrictions on the behavior of the metrics off of the ends in question and in particular does not require their geodesic completeness. As an application, we prove that the only complete connected gradient shrinking Ricci soliton asymptotic to a rotationally symmetric cone is the Gaussian soliton on $\mathbb{R}^n$.


Download Citation

Brett Kotschwar. Lu Wang. "Rigidity of asymptotically conical shrinking gradient Ricci solitons." J. Differential Geom. 100 (1) 55 - 108, May 2015.


Published: May 2015
First available in Project Euclid: 24 March 2015

zbMATH: 06438782
MathSciNet: MR3326574
Digital Object Identifier: 10.4310/jdg/1427202764

Rights: Copyright © 2015 Lehigh University


Vol.100 • No. 1 • May 2015
Back to Top