Pith Number

pith:7LPM4IG5

pith:2026:7LPM4IG5B766DXUYY3DCRM6KHN

not attested not anchored not stored refs resolved

Unbounded mean convex domains in Euclidean space

Jian Ge

The infimum of mean curvature on any disconnected boundary component of an unbounded mean convex domain in Euclidean space must be zero.

arxiv:2605.16802 v1 · 2026-05-16 · math.DG

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\pithnumber{7LPM4IG5B766DXUYY3DCRM6KHN}

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Claims

C1strongest claim

The infimum of the mean curvature on any disconnected boundary component of an unbounded mean convex domain in R^n must be zero.

C2weakest assumption

The domain is assumed to be mean convex (H ≥ 0) with sufficiently regular boundary to apply the maximum principle or comparison theorems at infinity; this is invoked in the contradiction argument when supposing inf H > 0 on a disconnected component.

C3one line summary

Proves that infimum of mean curvature on any disconnected boundary component of an unbounded mean convex domain in R^n is zero.

References

6 extracted · 6 resolved · 0 Pith anchors

[1] Croke and Bruce Kleiner 1992

[2] The structure of complete stable minimal surfaces in 3 -manifolds of non-negative scalar curvature 1980

[3] Mean Curvature in the Light of Scalar Curvature 2019

[4] David Hoffman and William H. Meeks, III. The strong halfspace theorem for minimal surfaces. Inventiones Mathematicae , 101(2):373--377, 1990 1990

[5] Riemannian manifolds with compact boundary 1981

Formal links

1 machine-checked theorem link

Cited by

1 paper in Pith

A Frankel type theorem in Euclidean and hyperbolic spaces

Receipt and verification

First computed	2026-05-20T00:03:22.980936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fadece20dd0ffde1de98c6c628b3ca3b69cddb6a7cd4d8d0dd81d031ff2a7227

Aliases

arxiv: 2605.16802 · arxiv_version: 2605.16802v1 · doi: 10.48550/arxiv.2605.16802 · pith_short_12: 7LPM4IG5B766 · pith_short_16: 7LPM4IG5B766DXUY · pith_short_8: 7LPM4IG5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7LPM4IG5B766DXUYY3DCRM6KHN \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: fadece20dd0ffde1de98c6c628b3ca3b69cddb6a7cd4d8d0dd81d031ff2a7227

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a2044284a7f59fc75decd5faa4c1cb392889f98792ed840a2285495519ada5f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-16T04:15:44Z",
    "title_canon_sha256": "77bf98136ede33dcf5f49fee85a28145dfbf69f21ec1dcb96d681ebb11dd98d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16802",
    "kind": "arxiv",
    "version": 1
  }
}