Pith Number

pith:QJLZQQD3

pith:2026:QJLZQQD3GRQ43H5E72DWHYHUYJ

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Terminal H\"older Closure in Curvature Estimates and its Application

Anji Tang

Replacing Young's inequality with Hölder's simplifies curvature estimates and extends to CMC hypersurfaces.

arxiv:2605.17466 v1 · 2026-05-17 · math.DG

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Claims

C1strongest claim

Replacing Young's inequality by Hölder's inequality at this stage yields a structurally simpler argument, a strictly smaller constant, and a natural extension to the constant-mean-curvature (CMC) setting. For strongly stable CMC hypersurfaces, the same Hölder mechanism produces an integral curvature estimate featuring two competing terms, separated by the condition |H|(1-θ)R ≤ 1.

C2weakest assumption

The argument starts from the standard preparatory gradient estimate (cited as known) and assumes the hypersurface is strongly stable; if either the preparatory estimate fails or strong stability is weakened, the Hölder closure step does not apply.

C3one line summary

Hölder closure of the SSY integral curvature estimate yields simpler arguments, strictly smaller constants than Young closure, and a quantitative reduction of CMC estimates to the minimal-surface case below a mean-curvature scale.

References

11 extracted · 11 resolved · 0 Pith anchors

[1] Simons,Minimal varieties in Riemannian manifolds, Ann 1968

[2] R. Schoen, L. Simon, and S.-T. Yau,Curvature estimates for minimal hypersurfaces, Acta Math. 134 (1975), 275–288 1975

[3] U. Massari and M. Miranda,Minimal Surfaces of Codimension One, North-Holland Math. Studies 91, North-Holland, Amsterdam, 1984 1984

[4] Moser,A new proof of De Giorgi’s theorem concerning the regularity problem for elliptic differential equations, Comm 1960

[5] C. Bellettini, O. Chodosh, and N. Wickramasekera,Curvature estimates and sheeting the- orems for weakly stable CMC hypersurfaces, Adv. Math. 352 (2019), 133–157 2019

Receipt and verification

First computed	2026-05-20T00:04:40.401069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

825798407b3461cd9fa4fe8763e0f4c25637b7037d515859484b3ac0e58ed13d

Aliases

arxiv: 2605.17466 · arxiv_version: 2605.17466v1 · doi: 10.48550/arxiv.2605.17466 · pith_short_12: QJLZQQD3GRQ4 · pith_short_16: QJLZQQD3GRQ43H5E · pith_short_8: QJLZQQD3

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QJLZQQD3GRQ43H5E72DWHYHUYJ \
  | 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: 825798407b3461cd9fa4fe8763e0f4c25637b7037d515859484b3ac0e58ed13d

Canonical record JSON

{
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    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-17T14:07:53Z",
    "title_canon_sha256": "8fca408087766c0eb68cfa0c86c4164fa3207fb8beb7fecf49620e08b7f45060"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17466",
    "kind": "arxiv",
    "version": 1
  }
}