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Ricci Flow Background
In this chapter we introduce and review some aspects of Ricci flow theoryRicci flowtheory that we shall need in the sequel. Excellent expositions of...
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Parabolic Frequency Monotonicity on Ricci Flow and Ricci-Harmonic Flow with Bounded Curvatures
In this paper, we study the monotonicity of parabolic frequency motivated by Baldauf and Kim (Parabolic frequency on Ricci flows. To appear in Int....
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Einstein Constraints and Ricci Flow A Geometrical Averaging of Initial Data Sets
This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given...
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Ricci flow with Ricci curvature and volume bounded below
We show that a simply-connected closed four-dimensional Ricci flow whose Ricci curvature is uniformly bounded below and whose volume does not...
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Harmonic Spinors in the Ricci Flow
This paper provides a new definition of the Ricci flow on closed manifolds admitting harmonic spinors. It is shown that Perelman’s Ricci flow entropy...
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Mean Curvature Flow in an Extended Ricci Flow Background
We consider a functional related to mean curvature flow in an ambient space which evolves by an extended Ricci flow from the perspective introduced...
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Ricci Solitons
This chapter provides the basic theory of Ricci flow, Ricci solitons, their examples, important properties and known results.
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Ricci Flow Conjugation of Initial Data Sets
In this chapter we address the main topic of these notes: Characterization of the parabolic conjugation between two distinct Einstein initial data...
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Scalar curvature along the Ricci flow
In this note, we prove a well-known conjecture on the Ricci flow under a curvature condition, which is a pinching between the Ricci and Weyl tensors...
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The Heterotic-Ricci Flow and Its Three-Dimensional Solitons
We introduce a novel curvature flow, the Heterotic-Ricci flow, as the two-loop renormalization group flow of the Heterotic string common sector and...
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Ricci Flow Under Kato-Type Curvature Lower Bound
In this work, we extend the existence theory of non-collapsed Ricci flows from point-wise curvature lower bound to Kato-type curvature lower bound....
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The Long-Time Existence of the Finslerian Ricci Flow
In this study, we demonstrate that any solution to the Finslerian Ricci flow encountering a singularity on a compact manifold is invariably...
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A Note on Kähler–Ricci Flow on Fano Threefolds
In this note, we show that the solution of Kähler–Ricci flow on every Fano threefold from Family No. 2.23 in the Mori–Mukai’s list develops type II...
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Weak scalar curvature lower bounds along Ricci flow
In this paper, we study Ricci flow on compact manifolds with a continuous initial metric. It was known from Simon (2002) that the Ricci flow exists...
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Entropy and Heat Kernel on Generalized Ricci Flow
We introduce analogous geometric quantities and prove some geometric and analytic bounds in [
1 ] to generalized Ricci flow. -
Matrix Li–Yau–Hamilton estimates under Ricci flow and parabolic frequency
We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the...
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Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow
We study the stability and instability of ALE Ricci-flat metrics around which a Łojasiewicz inequality is satisfied for a variation of Perelman’s
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Ancient Solutions of Ricci Flow with Type I Curvature Growth
Ancient solutions of the Ricci flow arise naturally as models for singularity formation. There has been significant progress towards the...