Yongjia Zhang
Published 2017-02-16Version 1
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 kappa-noncollapsing on all scales. This provides an evidence for Perelman's more general assertion that on a complete ancient solution with nonnegative curvature operator, bounded entropy is equivalent to kappa-noncollapsing.
The Ricci flow of the `RP3 geon' and noncompact manifolds with essential minimal spheres
The Existence of Type II Singularities for the Ricci Flow on $S^{n+1}$
Eigenvalues and energy functionals with monotonicity formulae under Ricci flow
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