Notes on Perelman's papers

Abstract

These are detailed notes on Perelman's papers "The entropy formula for the Ricci flow and its geometric applications" and "Ricci flow with surgery on three-manifolds".

216 pages, minor corrections made

Cited by in corpus (78)

• A compactness theorem for complete Ricci shrinkers
• Mean curvature flow with surgery
• Ricci flow on surfaces with conic singularities
• The minimal volume orientable hyperbolic 2-cusped 3-manifolds
• Contracting exceptional divisors by the Kähler-Ricci flow
• $W$-entropy formula for the Witten Laplacian on manifolds with time dependent metrics and potentials
• Distinguishing geometries using finite quotients
• C${}^{\ast }$-simple groups: amalgamated free products, HNN extensions, and fundamental groups of 3-manifolds
• Integer homology 3-spheres admit irreducible representations in SL(2,C)
• The Ricci flow on noncommutative two-tori
• On three-manifolds dominated by circle bundles
• Ricci flow on asymptotically Euclidean manifolds
• On Relativistic Generalization of Perelman's W-entropy and Statistical Thermodynamic Description of Gravitational Fields
• Mean curvature flow in a Ricci flow background
• Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces
• Ricci flow on open 3-manifolds and positive scalar curvature
• Hypersymplectic 4-manifolds, the $G_2$-Laplacian flow and extension assuming bounded scalar curvature
• On the conditions to extend Ricci flow(II)
• Almost Kaehler Ricci Flows and Einstein and Lagrange-Finsler Structures on Lie Algebroids
• Shi-type estimates and finite time singularities of flows of G${}_2$ structures
• On Supersymmetric Geometric Flows and ${\mathcal{R}}^2$ Inflation From Scale Invariant Supergravity
• Monotone Volume Formulas for Geometric Flows
• Geometric information flows and G. Perelman entropy for relativistic classical and quantum mechanical systems
• Formal matched asymptotics for degenerate Ricci flow neckpinches
• Geodesics on strong Kropina manifolds
• Ricci curvature, isoperimetry and a non-additive entropy
• Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity
• Bounds on exceptional Dehn filling II
• Algorithms and complexity for Turaev-Viro invariants
• $\epsilon$-Regularity and Structure of 4-dimensional Shrinking Ricci Solitons
• Geometric Flow of Bubbles
• Metric Flows with Neural Networks
• Classical and quantum geometric information flows and entanglement of relativistic mechanical systems
• Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity
• Orbit spaces of equivariantly formal torus actions of complexity one
• Metric Compatible or Noncompatible Finsler-Ricci Flows
• Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and $F(R,T,Q,T_m)$ gravity
• Local smoothing results for the Ricci flow in dimensions two and three
• Nonassociative Ricci flows, star product and R-flux deformed black holes, and swampland conjectures
• Smooth surfaces with non-simply-connected complements
• On the initial geometry of a vacuum cosmological spacetime
• Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies
• A simple proof of Perelman's collapsing theorem for 3-manifolds
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
• Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions
• Systoles and Dehn surgery for hyperbolic 3-manifolds
• Mixed curvature almost flat manifolds
• Kaluza--Klein gravity & cosmology emerging from G. Perelman's entropy functionals and quantum geometric information flows
• On the top-dimensional ${\ell }^2$-Betti numbers
• The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory
• Metrics with ${\lambda }_1(-\Delta +kR)\ge 0$ and flexibility in the Riemannian Penrose Inequality
• A characterization on separable subgroups of 3-manifold groups
• Off-diagonal deformations of regular Schwarzschild black holes and general relativistic G. Perelman thermodynamics
• Nonmetric geometric flows and quasicrystalline topological phases for dark energy and dark matter in $f(Q)$ cosmology
• Producing 3d Ricci flows with non-negative Ricci curvature via singular Ricci flows
• Long-time behavior of 3 dimensional Ricci flow -- A: Generalizations of Perelman's long-time estimates
• Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions
• Towers of regular self-covers and linear endomorphisms of tori
• Survey on L^2-invariants and 3-manifolds
• On the stable Cannon Conjecture
• Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows
• On the dynamical behaviour of the generalized Ricci flow
• Non-fibered L-space knots
• Isoperimetric problem and structure at infinity on Alexandrov spaces with nonnegative curvature
• A tree traversal algorithm for decision problems in knot theory and 3-manifold topology
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations
• Off-diagonal solutions in Einsteingravity modeling f(R) gravity and dynamical darkenergy vs Lambda CDM cosmology
• Treewidth, crushing, and hyperbolic volume
• Dynamical Equations and Lagrange--Ricci Flow Evolution on Prolongation Lie Algebroids
• Open and Discrete Maps with Piecewise Linear Branch Set Images are Piecewise Linear Maps
• Mean curvature flow in an extended Ricci flow background
• Perelman's invariant and collapse via geometric characteristic splittings
• Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature
• Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow
• K-contact manifolds with minimal closed Reeb orbits
• A New Geometric Flow on 3-Manifolds: the $K$-Flow
• Asymptotic cones and quantum gravity
• On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows