Pith Number

pith:CQYFSR4V

pith:2024:CQYFSR4V6HOUK6AWS6V6HP3JNJ

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Conformal Scalar-Flat Metrics with Prescribed Boundary Mean Curvature

Hongyi Sheng, Jiashu Shen

Local test functions establish solvability for most remaining cases of the boundary Yamabe problem left open by Escobar.

arxiv:2410.06302 v2 · 2024-10-08 · math.DG

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Claims

C1strongest claim

Through the construction of local test functions, we resolve most of the remaining open cases from Escobar's work and establish new solvability conditions.

C2weakest assumption

The local test functions can be chosen so that the associated energy functional satisfies the necessary inequalities to guarantee a critical point (implicit in the variational setup for the boundary Yamabe problem).

C3one line summary

Resolves most remaining open cases for scalar-flat conformal metrics with prescribed boundary mean curvature via local test function construction and new solvability conditions.

References

25 extracted · 25 resolved · 1 Pith anchors

[1] Diﬀerential Equations 259 (2015), no 2015 · doi:10.1016/j.jde.2015.04.011

[2] Thierry Aubin, ´Equations diﬀ´ erentielles non lin´ eaires et probl` eme de Yamabe concernant la courbure scalaire, J. Math. Pures Appl. (9) 55 (1976), no. 3, 269–296. MR0431287 1976

[3] Simon Brendle, Convergence of the Yamabe ﬂow in dimension 6 and higher , Invent. Math. 170 (2007), no. 3, 541–576, DOI 10.1007/s00222-007-0074-x. MR 2357502 2007 · doi:10.1007/s00222-007-0074-x

[4] Simon Brendle and Szu-Yu Sophie Chen, An existence theorem for the Yamabe problem on manifolds with boundary , J. Eur. Math. Soc. (JEMS) 16 (2014), no. 5, 991–1016, DOI 10.4171/JEMS/453. MR3210959 2014 · doi:10.4171/jems/453

[5] Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions 2010 · arXiv:0912.1302

Formal links

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Receipt and verification

First computed	2026-05-26T02:02:57.610192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1430594795f1dd45781697abe3bf696a733f04e922468216fa7d3094faf1d999

Aliases

arxiv: 2410.06302 · arxiv_version: 2410.06302v2 · doi: 10.48550/arxiv.2410.06302 · pith_short_12: CQYFSR4V6HOU · pith_short_16: CQYFSR4V6HOUK6AW · pith_short_8: CQYFSR4V

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CQYFSR4V6HOUK6AWS6V6HP3JNJ \
  | 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: 1430594795f1dd45781697abe3bf696a733f04e922468216fa7d3094faf1d999

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": "2024-10-08T19:23:26Z",
    "title_canon_sha256": "18ebf367e6ddbb44984ca89b8cd74cb7e19e1691fd6c38e24af6a9ff93a526b0"
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