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pith:FIDMBND5

pith:2026:FIDMBND5Y3PVJRXAFJEPNXSQDS

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Classification of the ruled surfaces that are critical points of the Dirichlet energy

Rafael L\'opez

Ruled surfaces in Euclidean space that are critical points of the Dirichlet energy are fully classified with explicit parametrizations.

arxiv:2605.14384 v1 · 2026-05-14 · math.DG

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3 Author claim open · sign in to claim

4 Citations open

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Claims

C1strongest claim

We classify all ruled surfaces in Euclidean space that are critical points of the Dirichlet energy, obtaining explicit parametrizations of these surfaces.

C2weakest assumption

The surfaces are assumed to be ruled (generated by straight lines) and immersed in Euclidean three-space; the Dirichlet energy is the standard integral of the squared norm of the first fundamental form.

C3one line summary

All ruled surfaces in Euclidean space that are critical points of the Dirichlet energy are classified with explicit parametrizations.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] E. Barbosa and L. C. Silva, Surfaces of constant anisotropic mean curvature with free boundary in revolution surfaces,Manuscr. Math.169(2022), 439–459 2022

[2] E. Catalan. Sur les surfaces r´ egl´ ees dont l?aire est un minimum,J. Math. Pure Appl.7(1842), 203–211

[3] J. A. G´ alvez, P. Mira and M. P. Tassi, Complete surfaces of constant anisotropic mean curva- ture,Adv. Math.428(2023), Paper No. 109137 2023

[4] J. Guo and C. Xia, Stable anisotropic capillary hypersurfaces in a half-space, arXiv:2301.03020 [math.DG]

[5] X. Jia, G. Wang and C. Xia, X. Zhang, Alexandrov’s theorem for anisotropic capillary hyper- surfaces in the half-space,Arch. Ration. Mech. Anal.247(2023), 25 2023

Receipt and verification

First computed	2026-05-17T23:39:07.689087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a06c0b47dc6df54c6e02a48f6de501cb27bd6c2400b3306c7dd9396a62c1ee5

Aliases

arxiv: 2605.14384 · arxiv_version: 2605.14384v1 · doi: 10.48550/arxiv.2605.14384 · pith_short_12: FIDMBND5Y3PV · pith_short_16: FIDMBND5Y3PVJRXA · pith_short_8: FIDMBND5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FIDMBND5Y3PVJRXAFJEPNXSQDS \
  | 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: 2a06c0b47dc6df54c6e02a48f6de501cb27bd6c2400b3306c7dd9396a62c1ee5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c0809a15a36eec20d85a3fa58c855032928f0e43a036584405b6b5ce89ff274",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-14T05:07:23Z",
    "title_canon_sha256": "e3a8f6256f4804108b4c1f467e7334a0339a3400a5671e5686ee6d66812234b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14384",
    "kind": "arxiv",
    "version": 1
  }
}