Abstract
In this paper we discuss the asymptotic entropy for ancient solutions to the Ricci flow. We prove a gap theorem for ancient solutions, which could be regarded as an entropy counterpart of Yokota’s work. In addition, we prove that under some assumptions on one time slice of a complete ancient solution with nonnegative curvature operator, finite asymptotic entropy implies κ-noncollapsing on all scales. This result is used by the author [21] to prove Perelman’s assertion that on an ancient solution to the Ricci flow with bounded nonnegative curvature operator, bounded entropy is equivalent to noncollapsing on all scales; see section 11 in [17].
Original language | English (US) |
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Pages (from-to) | 501-524 |
Number of pages | 24 |
Journal | Communications in Analysis and Geometry |
Volume | 29 |
Issue number | 2 |
DOIs | |
State | Published - 2021 |
Bibliographical note
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