Asset Details
Do you wish to reserve the book?
Geometry of shrinking Ricci solitons
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
Geometry of shrinking Ricci solitons
Do you wish to request the book?
Geometry of shrinking Ricci solitons
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
Geometry of shrinking Ricci solitons
2015
Overview
The main purpose of this paper is to investigate the curvature behavior of four-dimensional shrinking gradient Ricci solitons. For such a soliton $M$ with bounded scalar curvature $S$, it is shown that the curvature operator $\\text{Rm}$ of $M$ satisfies the estimate $|\\text{Rm}|\\leqslant cS$ for some constant $c$. Moreover, the curvature operator $\\text{Rm}$ is asymptotically nonnegative at infinity and admits a lower bound $\\text{Rm}\\geqslant -c(\\ln (r+1))^{-1/4}$, where $r$ is the distance function to a fixed point in $M$. As an application, we prove that if the scalar curvature converges to zero at infinity, then the soliton must be asymptotically conical. As a separate issue, a diameter upper bound for compact shrinking gradient Ricci solitons of arbitrary dimension is derived in terms of the injectivity radius.
Publisher
London Mathematical Society,Cambridge University Press
Subject
