As on arXiv
Abstract
We prove an analogue statement to an estimate by De Lellis-Müller in on the standard Minkowski lightcone. More precisely, we show that under some additional assumptions, any spacelike cross section of the standard lightcone is -close to a round surface provided the trace-free part of a scalar second fundamental form is sufficiently small in . To determine the correct intrinsically round cross section of reference, we define an associated -vector, which transforms equivariantly under Lorentz transformations in the restricted Lorentz group. A key step in the proof consists of a geometric, scaling invariant estimate, and we give two different proofs. One utilizes a recent characterization of singularity models of null mean curvature flow along the standard lightcone by the author, while the other is heavily inspired by an almost-Schur lemma by De Lellis-Topping.
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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 2021, plus the canon.
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An area growth argument for null mean curvature flow along the standard de Sitter lightcone
Topics Physics, Singularities · Same author Markus Wolff · Shared terms “lightcone”, “flow along”, “null mean”
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Ricci flow on surfaces along the standard lightcone in the -Minkowski spacetime
Topics Singularities · Same author Markus Wolff · Shared terms “standard lightcone”, “Minkowski lightcone”, “cross section”
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On the evolution of hypersurfaces along their inverse spacetime mean curvature
Topics Physics · Same author Markus Wolff · Shared terms “null mean”
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Foliations of asymptotically Schwarzschildean lightcones by surfaces of constant spacetime mean curvature
Topics Mean curvature flow · Same author Markus Wolff · Shared terms “lightcone”, “null mean”
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Invariant -translators in Lorentz-Minkowski space
Topics Physics · Shared terms “Lorentz”, “Minkowski”, “spacelike”
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A capillary problem for spacelike mean curvature flow in a cone of Minkowski space
Topics Physics · Shared terms “lightcone”, “Minkowski”, “spacelike”
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Spacelike Brakke flows with boundary in pseudo-Euclidean space
Topics Physics, Singularities · Shared terms “spacelike”
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Foliations by constant spacetime mean curvature surfaces for asymptotically hyperboloidal initial data sets
Topics Physics · Shared terms “inspired”
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In the guidebook
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