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The Ricci Flow: An Introduction
Bennett Chow,Dan Knopf +1 more
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The Ricci flow of special geometries Special and limit solutions Short time existence Maximum principles The Ricci Flow on surfaces Three-manifolds of positive Ricci curvature Derivative estimates Singularities and the limits of their dilations Type I singularities as discussed by the authors.Abstract:
The Ricci flow of special geometries Special and limit solutions Short time existence Maximum principles The Ricci flow on surfaces Three-manifolds of positive Ricci curvature Derivative estimates Singularities and the limits of their dilations Type I singularities The Ricci calculus Some results in comparison geometry Bibliography Index.read more
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The Asymptotic Safety Scenario in Quantum Gravity
Max Niedermaier,Martin Reuter +1 more
TL;DR: In this paper, a renormalizable quantum theory of the gravitational field is presented, which reconciles asymptotically safe couplings with unitarity, based on symmetry truncations and from truncated flow of the effective average action.
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Self-Similar Groups
TL;DR: In this article, the authors define limit spaces, limit spaces and limit spaces in algebraic theory, and use them to define Iterated Monodromy groups (IMG) groups.
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Notes on Perelman's papers
Bruce Kleiner,John Lott +1 more
TL;DR: In this paper, the Ricci flow with surgery with surgery was shown to die in a finite time, which is the case for the Poincar´ e Conjecture.
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Notes on Perelman's papers
Bruce Kleiner,John Lott +1 more
TL;DR: Perelman as discussed by the authors described the entropy formula for the Ricci flow and its geometric applications, including its application in surgery on three-manifolds, and gave detailed notes on Perelman's papers.
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A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow
Huai-Dong Cao,Xi-Ping Zhu +1 more
TL;DR: In this article, a complete proof of the Poincare and geometrization conjectures of Ricci flow is given, based on the accumulative works of many geometric analysts in the past thirty years.
References
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Linear and Quasilinear Equations of Parabolic Type
TL;DR: In this article, the authors considered a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtained parameter dependent time decay estimates of the difference between the solutions of the solution of a quasi-linear parabolic equation and the corresponding linear parabolic equations.
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Geometric Measure Theory
TL;DR: In this article, Grassmann algebras of a vectorspace have been studied in the context of the calculus of variations, and a glossary of some standard notations has been provided.
Book
Shock Waves and Reaction-Diffusion Equations
TL;DR: In this paper, the basics of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by Charles Conley, are presented in a way accessible to a wider audience than just mathematicians.
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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