Paper · Jun 2, 2018

Parabolic Dimensional Reductions of 11D Supergravity

Teng Fei, Bin Guo, Duong H. Phong

math.DGarXiv:1806.00583
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Abstract

Ansatze are constructed under which the solutions of 11D supergravity must be stationary points of a parabolic flow on a Riemannian manifold . This parabolic flow turns out to be the Ricci flow coupled to a scalar field, a -form, and a -form. This allows the introduction of techniques from parabolic partial differential equations to the search of solutions to 11D supergravity. As a first step, Shi-type estimates and criteria for the long-time existence of the flow are established.

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Submitted
Jun 2, 2018
Subjects
math.DG, hep-th, math-ph, math.AP
Journal
Analysis & PDE 14 (2021) 1333-1361
DOI
10.2140/apde.2021.14.1333

Comments: 36 pages, comments welcome!

Ricci flowLong-time existence & convergencePhysics

Its neighbourhood

Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Ricci flow on asymptotically Euclidean manifolds (Yu Li, 2016)8Li 2016 Compactness of Kahler-Ricci solitons on Fano manifolds (Bin Guo, Duong H. Phong, Jian Song et al., 2018)7Guo 2018 New curvature flows in complex geometry (Duong H. Phong, Sebastien Picard and Xiangwen Zhang, 2018)2Phong 2018 Unification of the Kähler-Ricci and Anomaly flows (Teng Fei and Duong H. Phong, 2019)4Fei 2019 On the Kahler-Ricci flow on Fano manifolds (Bin Guo, Duong H. Phong and Jacob Sturm, 2020)6Guo 2020 Estimates for a geometric flow for the Type IIB string (Teng Fei, Duong H. Phong, Sebastien Picard et al., 2020)3Fei 2020 Symplectic geometric flows (Teng Fei and Duong H. Phong, 2021)5Fei 2021 Diameter estimates in Kähler geometry (Bin Guo, Duong H. Phong, Jian Song et al., 2022)1Guo 2022
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Diameter estimates in Kähler geometry

    Bin Guo, Duong H. Phong, Jian Song et al.

    Topics Long-time existence & convergence · Same authors Bin Guo, Duong H. Phong

  2. New curvature flows in complex geometry

    Duong H. Phong, Sebastien Picard and Xiangwen Zhang

    Topics Physics · Same author Duong H. Phong · Shared terms “partial differential”, “differential equation”

  3. Estimates for a geometric flow for the Type IIB string

    Teng Fei, Duong H. Phong, Sebastien Picard et al.

    Topics Ricci flow · Same authors Teng Fei, Duong H. Phong

  4. Unification of the Kähler-Ricci and Anomaly flows

    Teng Fei and Duong H. Phong

    Topics Ricci flow · Same authors Teng Fei, Duong H. Phong

  5. Symplectic geometric flows

    Teng Fei and Duong H. Phong

    Topics Ricci flow · Same authors Teng Fei, Duong H. Phong

  6. On the Kahler-Ricci flow on Fano manifolds

    Bin Guo, Duong H. Phong and Jacob Sturm

    Topics Ricci flow · Same authors Bin Guo, Duong H. Phong

  7. Compactness of Kahler-Ricci solitons on Fano manifolds

    Bin Guo, Duong H. Phong, Jian Song et al.

    Same authors Bin Guo, Duong H. Phong

  8. Ricci flow on asymptotically Euclidean manifolds

    Yu Li

    Topics Physics, Long-time existence & convergence

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci flow Hamilton's Ricci flow evolves a Riemannian metric by minus twice its Ricci curvature. It is a nonlinear heat equation for geometry: it spreads… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Long-time existence & convergence A geometric flow either runs forever or stops because something blows up. Extension criteria say which quantity must blow up at a finite singular… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Physics Ricci flow first appeared in physics, as the leading-order renormalization-group flow of the string sigma model (Friedan, 1980). Start with: Nonlinear Models in 2+ε Dimensions (Friedan, 1980)

In the guidebook

  1. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  2. 10A.12
    Curve Shortening and Minimal DiscsBook 10A · Three-Manifolds and Geometrization

    How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.

  3. 11A.1
    The Equation and Its First SolutionsBook 11A · The Ricci Flow: Existence and Maximum Principles

    A heat equation for the metric: spheres, cylinders and scaling.