Pith Number

pith:5OMSHEX6

pith:2026:5OMSHEX67Y2SGIPMUFTY267K2Y

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Some sharp Schwarz type estimates and their applications in Banach spaces

Hidetaka Hamada, Megha Kundathil, Ramakrishnan Vijayakumar, Shaolin Chen

Improved sharp Schwarz estimates enable new boundary and point-to-point lemmas for holomorphic mappings in Banach spaces.

arxiv:2605.17237 v1 · 2026-05-17 · math.CV

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Claims

C1strongest claim

We improve upon the main results obtained by Osserman and Chen et al. Based on these sharp estimates, we derive several sharp boundary Schwarz type lemmas for holomorphic mappings in Banach spaces, as well as for solutions to certain classes of elliptic partial differential equations on the Euclidean unit ball in C^n or on the unit disk in C.

C2weakest assumption

The derivations presuppose that the holomorphic mappings under consideration map the unit ball into itself (or satisfy analogous normalization conditions) and that the prior sharp estimates of Osserman and Chen et al. remain valid as the starting point for the new boundary and point-to-point versions.

C3one line summary

Improves Osserman and Chen et al. Schwarz lemmas in Banach spaces, derives sharp boundary versions for holomorphic maps and PDE solutions, and applies them to Minda inequalities and subball bounds.

References

42 extracted · 42 resolved · 0 Pith anchors

[1] L. V . Ahlfors, An extension of Schwarz’s lemma,Trans. Amer. Math. Soc.,43(1938), 359–364. [1] 1938

[2] Begehr, Dirichlet problems for the biharmonic equation,Gen 2005

[3] M. Bonk and A. Eremenko, Covering properties of meromorphic functions, negative curvature and spherical geometry,Ann. Math.,152(2000), 551–592. [1] 2000

[4] F. Bracci, D. Kraus and O. Roth, A new Schwarz-Pick lemma at the boundary and rigidity of holomorphic maps, Adv. Math.,432(2023), Article ID 109262, 41pp. [1] 2023

[5] D. M. Burns and S. G. Krantz, Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary,J. Amer. Math. Soc.,7(1994), 661–676. [1] 1994

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:46.895591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb992392fefe352321eca1678d7bead622001ec1bf2e04f66b72ca83f9dafb53

Aliases

arxiv: 2605.17237 · arxiv_version: 2605.17237v1 · doi: 10.48550/arxiv.2605.17237 · pith_short_12: 5OMSHEX67Y2S · pith_short_16: 5OMSHEX67Y2SGIPM · pith_short_8: 5OMSHEX6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5OMSHEX67Y2SGIPMUFTY267K2Y \
  | 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: eb992392fefe352321eca1678d7bead622001ec1bf2e04f66b72ca83f9dafb53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e121ebd064ac5c43e6cb8b741cdf86edea0a1e5d064ed7d9616ce3a19c1f973e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2026-05-17T03:17:17Z",
    "title_canon_sha256": "12338b3ac5dc49fe6f6c8de31a2b06afb5e3dfeabea141343dafb5c5d326e674"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17237",
    "kind": "arxiv",
    "version": 1
  }
}