Paper · Oct 15, 2019

Isoperimetric problems for spacelike domains in generalized Robertson-Walker spaces

Ben Lambert, Julian Scheuer

math.DGWider flowsarXiv:1910.06696
View PDF View HTML arXiv page

As on arXiv

Abstract

We use a locally constrained mean curvature flow to prove the isoperimetric inequality for spacelike domains in generalized Robertson-Walker spaces satisfying the null convergence condition.

View PDF View HTML arXiv page
Submitted
Oct 15, 2019
Subjects
math.DG, math.AP
Journal
J. Evol. Equ. 21, no. 1, (2021), p. 377-389
DOI
10.1007/s00028-020-00584-z

Comments: 10 pages

Mean curvature flowVolume-preserving & constrained flowsGeometric inequalitiesPhysics

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 A geometric inequality for convex free boundary hypersurfaces in the unit ball (Ben Lambert and Julian Scheuer, 2016)6Lambert 2016 On symmetries of generalized Robertson-Walker Space-times and applications (H. K. El-Sayied, S. Shenawy and N. Syied, 2016)1El-Sayied 2016 Locally constrained inverse curvature flows (Julian Scheuer and Chao Xia, 2017)2Scheuer 2017 Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball (Julian Scheuer, Guofang Wang and Chao Xia, 2018)5Scheuer 2018 The Minkowski inequality in de Sitter space (Julian Scheuer, 2019)4Scheuer 2019 Mean curvature flow of graphs in Generalized Robertson-Walker spacetimes with perpendicular Neumann boundary condition (Jorge Lira and Fernanda Roing, 2022)8Lira 2022 The quermassintegral preserving mean curvature flow in the sphere (Esther Cabezas-Rivas and Julian Scheuer, 2022)7Cabezas-Riva 2022 A capillary problem for spacelike mean curvature flow in a cone of Minkowski space (Wilhelm Klingenberg, Ben Lambert and Julian Scheuer, 2023)3Klingenberg 2023
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. On symmetries of generalized Robertson-Walker Space-times and applications

    H. K. El-Sayied, S. Shenawy and N. Syied

    Shared terms “Walker space”, “generalized Robertson”, “Robertson Walker”

  2. Locally constrained inverse curvature flows

    Julian Scheuer and Chao XiaWider flows

    Topics Geometric inequalities, Volume-preserving & constrained flows, Physics · Same author Julian Scheuer · Shared terms “locally constrained”, “isoperimetric”

  3. A capillary problem for spacelike mean curvature flow in a cone of Minkowski space

    Wilhelm Klingenberg, Ben Lambert and Julian ScheuerWider flows

    Topics Physics · Same authors Ben Lambert, Julian Scheuer · Shared terms “spacelike”

  4. The Minkowski inequality in de Sitter space

    Julian ScheuerWider flows

    Topics Geometric inequalities, Volume-preserving & constrained flows, Physics · Same author Julian Scheuer · Shared terms “locally constrained”

  5. Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball

    Julian Scheuer, Guofang Wang and Chao XiaWider flows

    Topics Geometric inequalities, Volume-preserving & constrained flows · Same author Julian Scheuer · Shared terms “isoperimetric”, “locally constrained”

  6. A geometric inequality for convex free boundary hypersurfaces in the unit ball

    Ben Lambert and Julian ScheuerWider flows

    Topics Geometric inequalities · Same authors Ben Lambert, Julian Scheuer

  7. The quermassintegral preserving mean curvature flow in the sphere

    Esther Cabezas-Rivas and Julian ScheuerWider flows

    Topics Geometric inequalities, Volume-preserving & constrained flows, Physics · Same author Julian Scheuer

  8. Mean curvature flow of graphs in Generalized Robertson-Walker spacetimes with perpendicular Neumann boundary condition

    Jorge Lira and Fernanda RoingWider flows

    Topics Mean curvature flow · Shared terms “generalized Robertson”, “Robertson Walker”, “convergence condition”

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.

Mean curvature flow Wider flows A hypersurface moves in the direction of its mean curvature vector, which decreases area as fast as possible in the L² sense. Start with: Flow by mean curvature of convex surfaces into spheres (Huisken, 1984) Volume-preserving & constrained flows Wider flows Curvature flows with a constraint: subtract the average of the mean curvature and the enclosed volume stays fixed while area decreases, so spheres… Start with: On an area-preserving evolution equation for plane curves (Gage, 1986) Geometric inequalities Sharp inequalities between area, volume and integrals of curvature, with equality only for round spheres. Start with: Mean curvature flow and geometric inequalities (Topping, 1998) 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. 6A.10
    Curve Shortening and the First Geometric FlowsBook 6A · The Heat Equation and Its Relatives

    Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.