Pith Number

pith:5GJCBPUA

pith:2026:5GJCBPUAAMFXWIWU73L6RHU4VP

not attested not anchored not stored refs pending

Optimal Asymptotic Behavior at Infinity for Solutions of the Supercritical Lagrangian Mean Curvature Equation in Exterior Domains

Jiguang Bao, Qinfeng Jiang

Solutions to the supercritical Lagrangian mean curvature equation in two dimensions converge to quadratic polynomials at infinity under merely Lipschitz perturbations that decay at any positive rate.

arxiv:2604.26246 v2 · 2026-04-29 · math.AP

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\usepackage{pith}
\pithnumber{5GJCBPUAAMFXWIWU73L6RHU4VP}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

This work generalizes the convergence results in [BJ2026], where f is required to be at least C^3 and β>2. Moreover, all asymptotic results established in this paper are optimal.

C2weakest assumption

The perturbation f is Lipschitz continuous and satisfies f(x) = O(|x|^{-β}) for some β > 0 at infinity, with |θ| in (0, π) a constant phase, and the equation holds on exterior domains in R^2.

C3one line summary

Solutions to the supercritical Lagrangian mean curvature equation in 2D exterior domains exhibit optimal asymptotic behavior at infinity under Lipschitz perturbations decaying at any positive rate.

Receipt and verification

First computed	2026-06-09T01:05:18.227686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e99220be80030b7b22d4fed7e89e9cabc4164773d64d1fa8140a9c430c6ae43f

Aliases

arxiv: 2604.26246 · arxiv_version: 2604.26246v2 · doi: 10.48550/arxiv.2604.26246 · pith_short_12: 5GJCBPUAAMFX · pith_short_16: 5GJCBPUAAMFXWIWU · pith_short_8: 5GJCBPUA

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5GJCBPUAAMFXWIWU73L6RHU4VP \
  | 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: e99220be80030b7b22d4fed7e89e9cabc4164773d64d1fa8140a9c430c6ae43f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43a577c1d41e38f4e7cee1a4b9be91c0d530b087508ced5dafdd7af5835091cb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-04-29T03:04:02Z",
    "title_canon_sha256": "b7b9383787a19d003a05198aa01a40da1b618ac0e8022b3a4f5c5e8017ba64d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26246",
    "kind": "arxiv",
    "version": 2
  }
}