Backwards Uniqueness for the Ricci Flow
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In this article, the authors prove a backwards uniqueness theorem for solutions to the Ricci flow and prove that the isometry group of a solution cannot expand within the lifetime of the solution.Abstract:
In this paper, we prove a backwards uniqueness theorem for solutions to the Ricci flow. A particular consequence is that the isometry group of a solution cannot expand within the lifetime of the solution.read more
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Laplacian flow for closed G2 structures: Shi-type estimates, uniqueness and compactness
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Uniqueness of self-similar shrinkers with asymptotically conical ends
TL;DR: In this article, the uniqueness of smooth embedded selfshrinkers asymptotic to generalized cylinders of infinite order was shown and non-rotationally symmetric self-shrinking ends were constructed with rate as fast as any given polynomial.
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Rigidity of asymptotically conical shrinking gradient Ricci solitons
Brett Kotschwar,Lu Wang +1 more
TL;DR: In this paper, it was shown that if two gradient shrinking Ricci solitons are asymptotic along some end of each to the same regular cone, then the soliton metrics must be isometric on some neighborhoods of infinity of these ends.
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Ricci flow of homogeneous manifolds
TL;DR: In this paper, a dynamical system defined on a subset of the variety of Lie algebras, parameterizing the space of all simply connected homogeneous spaces of dimension ρ ≥ 0, with a ρ-dimensional isotropy, which is proved to be equivalent in a precise sense to the Ricci flow, is presented.
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Posted Content
The entropy formula for the Ricci flow and its geometric applications
TL;DR: In this article, a monotonic expression for Ricci flow, valid in all dimensions and without curvature assumptions, is presented, interpreted as an entropy for a certain canonical ensemble.
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Three-manifolds with positive Ricci curvature
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The Ricci Flow: An Introduction
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