Pith. sign in

REVIEW 2 cited by

Min-max minimal surfaces, horizons and electrostatic systems

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 1912.08600 v3 pith:7IJVD22N submitted 2019-12-18 math.DG gr-qc

Tiarlos Cruz , Vanderson Lima , Alexandre de Sousa This is my paper · ORCID
classification math.DGgr-qc
keywords indexminimalareahorizonsinequalitymin-maxsurfacessystems
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We present a connection between minimal surfaces of index one and General Relativity. First, we show that for a certain class of (electro)static systems, each of its unstable horizons is the solution of a one-parameter min-max problem for the area functional, in particular it has index one. We also obtain an inequality relating the area and the charge of a minimal surface of index one in a Cauchy data satisfying the Dominant Energy Condition for non-electromagnetic matter fields. Moreover, we explore a global version of this inequality, and the rigidity in the case of the equality, using a result proved by Marques and Neves.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Some splitting and rigidity results for sub-static spaces

    math.DG 2024-12 unverdicted novelty 7.0 of 10

    New rigidity theorems: boundary integral inequalities generalizing Boucher-Gibbons-Horowitz, local and end splitting theorems, and a Liouville bound for static wave maps in sub-static spaces.

  2. Sharp lower bound for the charged Hawking mass in the electrostatic space

    math.DG 2025-07 conditional novelty 6.0 of 10

    Stable surfaces in electrostatic space-times have charged Hawking mass bounded below by an explicit formula in area, charge, and the cosmological constant, with equality cases realized by photon spheres and black hole...

Pith tools