Pith Number

pith:4XBFEXII

pith:2026:4XBFEXIILSVPVPWLLCHHZZYJRK

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Energy identity for stationary biharmonic mappings into spheres in supercritical dimensions

Chang-Lin Xiang, Changyou Wang, Chang-Yu Guo

Stationary biharmonic maps into spheres satisfy an energy identity when the domain dimension is at least five.

arxiv:2605.14052 v1 · 2026-05-13 · math.AP · math.DG

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\pithnumber{4XBFEXIILSVPVPWLLCHHZZYJRK}

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3 Author claim open · sign in to claim

4 Citations open

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Claims

C1strongest claim

we establish the energy identity for stationary biharmonic maps into spheres in supercritical dimensions n≥5

C2weakest assumption

The maps are stationary biharmonic and the dimension satisfies n≥5; the adaptation of the Lin-Rivière strategy succeeds without further restrictions on the maps or domain.

C3one line summary

Establishes the energy identity for stationary biharmonic maps into spheres in supercritical dimensions n ≥ 5.

References

37 extracted · 37 resolved · 0 Pith anchors

[1] De Lellis , Rectifiable sets, densities and tangent measures 2008

[2] S. Y. A. Chang, L. Wang and P. C. Yang, A regularity theory of biharmonic maps. Commun. Pure Appl. Math. 52(9) (1999), 1113-1137 1999

[3] Y. Chen and M. Zhu , Bubbling analysis for extrinsic biharmonic maps from general Riemannian 4-manifolds. Sci. China Math. 66 (2023), no. 3, 581-600 2023

[4] C. L. Evans, Partial regularity for stationary harmonic maps into spheres. Arch. Rat. Mech. Anal. 116 (1991), 101-163 1991

[5] W. Y. Ding and G. Tian , Energy identity for a class of approximate harmonic maps from surfaces. Comm. Anal. Geom. 3 (1995), 543-554 1995

Receipt and verification

First computed	2026-05-17T23:39:12.630006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5c2525d085caafabecb588e7ce7098aac0d75cd6c862f6e134480a3e4c3c2fc

Aliases

arxiv: 2605.14052 · arxiv_version: 2605.14052v1 · doi: 10.48550/arxiv.2605.14052 · pith_short_12: 4XBFEXIILSVP · pith_short_16: 4XBFEXIILSVPVPWL · pith_short_8: 4XBFEXII

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4XBFEXIILSVPVPWLLCHHZZYJRK \
  | 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: e5c2525d085caafabecb588e7ce7098aac0d75cd6c862f6e134480a3e4c3c2fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94bc9ffef29114cc55abc5946a8c9f483f4410a8c60e4e051f5adf439b6c5cfc",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T19:19:21Z",
    "title_canon_sha256": "19b502ede88d8780ffcd1fd0f42c0a613c7ee22978a902fcb217b386f4e83893"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14052",
    "kind": "arxiv",
    "version": 1
  }
}