Pith. sign in

REVIEW 1 cited by

The Graphs Cases of the Riemannian Positive Mass and Penrose Inequalities in All Dimensions

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1010.4256 v1 pith:5MSTRF35 submitted 2010-10-20 math.DG gr-qc

Mau-Kwong George Lam This is my paper · ORCID
classification math.DGgr-qc
keywords riemannianmasscurvaturegraphsinequalitymanifoldspenrosepositive
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We consider complete asymptotically flat Riemannian manifolds that are the graphs of smooth functions over $\mathbb R^n$. By recognizing the scalar curvature of such manifolds as a divergence, we express the ADM mass as an integral of the product of the scalar curvature and a nonnegative potential function, thus proving the Riemannian positive mass theorem in this case. If the graph has convex horizons, we also prove the Riemannian Penrose inequality by giving a lower bound to the boundary integrals using the Aleksandrov-Fenchel inequality.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A new boundary mass for asymptotically flat half-manifolds

    math.DG 2026-06 unverdicted novelty 7.0 of 10

    Introduces a boundary analogue of the Gauss-Bonnet-Chern mass for asymptotically flat half-manifolds, proves it is well-defined, establishes positive mass theorems for graphical and conformally flat graphs, and provid...

Pith tools