Proof of a null Penrose conjecture using a new quasi-local mass

Roesch, Henri

doi:10.4310/cag.2021.v29.n8.a5

Cited by 2 publications

(1 citation statement)

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“…[19]. Moreover, as it is the case for the Minkowski and Schwarzschild lightcone, see [24] and [17] respectively, we note that any spacelike cross section Σ of N , i.e., a 2-dimensional, spacelike submanifold of N that intersects any integral curve of L exactly once, can be uniquely identified with a conformally round metric. To see this, recall that L(ρ) = 1, so ρ restricts to an affine parameter along N , and we may thus uniquely identify Σ with a function ω : Proposition 1], we find that the induced metric γ = γ ω and null second fundamental form χ = χ ω (with respect to L) of Σ = Σ ω satisfy…”

Section: In Particularmentioning

confidence: 77%

Ricci flow on surfaces along the standard lightcone in the $$3+1$$-Minkowski spacetime

Wolff

2023

Calc. Var.

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Identifying any conformally round metric on the 2-sphere with a unique cross section of the standard lightcone in the $$3+1$$ 3 + 1 -Minkowski spacetime, we gain a new perspective on 2d-Ricci flow on topological spheres. It turns out that in this setting, Ricci flow is equivalent to a null mean curvature flow first studied by Roesch–Scheuer along null hypersurfaces. Exploiting this equivalence, we can translate well-known results from 2d-Ricci flow first proven by Hamilton into a full classification of the singularity models for null mean curvature flow in the Minkowski lightcone. Conversely, we obtain a new proof of Hamilton’s classical result using only the maximum principle.

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Section: In Particularmentioning

confidence: 77%