Pith Number

pith:PON6P4RF

pith:2026:PON6P4RFTYI2E3FQDHOWZ7X55N

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On Caratheodory prime ends extension for unclosed Orlicz-Sobolev classes

Evgeny Sevost'yanov, Zarina Kovba

Open and discrete mappings from Orlicz-Sobolev classes admit continuous extensions to prime ends even without preserving the domain boundary.

arxiv:2604.15026 v2 · 2026-04-16 · math.CV

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Claims

C1strongest claim

The results we obtain concern the case when the mappings are open, discrete, but not closed (not preserving the boundary of a domain). These results generalize the well-known results of Caratheodory on boundary extension of conformal mappings.

C2weakest assumption

The mappings are assumed to belong to suitable Orlicz-Sobolev classes and to be open and discrete (but not closed), with the underlying domain admitting a prime-end compactification.

C3one line summary

Proves prime-end boundary extensions for open discrete unclosed mappings in Orlicz-Sobolev classes, extending Carathéodory's theorem.

References

29 extracted · 29 resolved · 0 Pith anchors

[1] - Analysis and Mathematical Physics 9:4, 2019, 1941-1975 2019

[2] Uber die Begrenzung der einfachzusammenh\ 1913

[3] Collingwood, E.F. and A.J. Lohwator : The Theory of Cluster Sets. -- Cambridge Tracts in Math. and Math. Physics 56, Cambridge Univ. Press, Cambridge, 1966 1966

[4] - Complex Variables and Elliptic Equations 55: 1--3, 2010, 61--90 2010

[5] Sevost'yanov: On boundary-non-preserving mappings with Poletsky inequality 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:38.080781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b9be7f2259e11a26cb019dd6cfefdeb680f4cad44e90d2d8b26d471ac8b9b9f

Aliases

arxiv: 2604.15026 · arxiv_version: 2604.15026v2 · doi: 10.48550/arxiv.2604.15026 · pith_short_12: PON6P4RFTYI2 · pith_short_16: PON6P4RFTYI2E3FQ · pith_short_8: PON6P4RF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PON6P4RFTYI2E3FQDHOWZ7X55N \
  | 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: 7b9be7f2259e11a26cb019dd6cfefdeb680f4cad44e90d2d8b26d471ac8b9b9f

Canonical record JSON

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    "abstract_canon_sha256": "0a62acf87d0cd5dd97020b66db37ee4968b9e3ba89c2cc0e46b53094a1885cf6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2026-04-16T13:55:27Z",
    "title_canon_sha256": "9025e77c185ec5d986a4d96b046cf73ad626f455dc82248341b3ee9d790e137b"
  },
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  "source": {
    "id": "2604.15026",
    "kind": "arxiv",
    "version": 2
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}