Pith Number

pith:RWTQNISA

pith:2026:RWTQNISA3UR6QGOMFG2I4O5LOV

not attested not anchored not stored refs pending

The $\sigma_k$-Yamabe problem revisited

Guofang Wang, Wei Wei, Yuxin Ge

If a closed manifold has positive Yamabe constant and positive σ₂-Yamabe constant, then the latter is achieved by a conformal metric.

arxiv:2605.05414 v2 · 2026-05-06 · math.DG · math.AP

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Record completeness

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4 Citations open

5 Replications open

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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

We prove that on a closed manifold (M,[g₀]) with positive Yamabe constant Y₁(M,[g₀])>0, the σ₂-Yamabe constant Y₂(M,[g₀]) is achieved by a conformal metric g ∈ [g₀], which in particular solves the σ₂-Yamabe problem, assuming Y₂(M,[g₀])>0.

C2weakest assumption

The assumption that Y₂(M,[g₀]) > 0 together with the restriction to metrics with R_g > 0 in the definition of the infimum; without R_g > 0 the conclusions can fail as shown in the paper.

C3one line summary

On closed manifolds with Y₁ > 0 and Y₂ > 0, the σ₂-Yamabe constant is achieved by a conformal metric with positive scalar curvature, and the two infima coincide.

Receipt and verification

First computed	2026-05-20T00:05:46.046040Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8da706a240dd23e819cc29b48e3bab75523f04fa40db4865a29afbf8e6cc0c3e

Aliases

arxiv: 2605.05414 · arxiv_version: 2605.05414v2 · doi: 10.48550/arxiv.2605.05414 · pith_short_12: RWTQNISA3UR6 · pith_short_16: RWTQNISA3UR6QGOM · pith_short_8: RWTQNISA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RWTQNISA3UR6QGOMFG2I4O5LOV \
  | 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: 8da706a240dd23e819cc29b48e3bab75523f04fa40db4865a29afbf8e6cc0c3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee114037d0f7007381c99fc67cbed061199fb9ddd7251e3f9bf73654e1d554c0",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-06T20:13:50Z",
    "title_canon_sha256": "04a2362296a64b2527e144a0be13529c73555ccd58cf2d28f495589717d00883"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.05414",
    "kind": "arxiv",
    "version": 2
  }
}