Pith Number

pith:CAIPD2JX

pith:2026:CAIPD2JXZNMS2IXY4BAFIBIO5K

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Blaschke operations on log-concave functions and affine isoperimetric inequalities

Effrosyni Chasioti, Steven Hoehner

Blaschke addition on log-concave functions produces affine isoperimetric inequalities with radial maximizers.

arxiv:2605.17688 v1 · 2026-05-17 · math.FA · math.MG

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Record completeness

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Claims

C1strongest claim

We prove affine isoperimetric inequalities for log-concave functions; in particular, the functional affine surface area is maximized, under fixed first quermassintegral, by radially symmetric functions, and satisfies a Blaschke-concavity property.

C2weakest assumption

The surface area measures arising from the first variation formula of Falah and Rotem are additive, which is used to define the canonical Blaschke sum uniquely up to translation (abstract, paragraph 2).

C3one line summary

Defines canonical Blaschke operations on log-concave functions and derives associated affine isoperimetric inequalities plus Kneser-Süss-type results.

References

31 extracted · 31 resolved · 0 Pith anchors

[1] Applebaum.Probability on Compact Lie Groups, volume 70 ofProbability Theory and Stochastic Mod- elling 2014

[2] G. Bianchi, R. J. Gardner, and P. Gronchi. Symmetrization in geometry.Advances in Mathematics, 306:51– 88, 2017. 4 2017

[3] S. Bobkov, A. Colesanti, and I. Fragal` a. Quermassintegrals of quasi-concave functions and generalized Pr´ ekopa–Leindler inequalities.Manuscripta math., 143:131–169, 2014. 2 2014

[4] D. Bucur, I. Fragal` a, and J. Lamboley. Optimal convex shapes for concave functionals.ESIAM: Control, Optimisation and Calculus of Variations, 18:693–711, 2012. 2 2012

[5] U. Caglar, M. Fradelizi, O. Guedon, J. Lehec, C. Sch¨ utt, and E. M. Werner. Functional versions ofLp-affine surface area and entropy inequalities.International Mathematics Research Notices, 4:1223–12 2016

Formal links

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Receipt and verification

First computed	2026-05-20T00:04:52.860620Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1010f1e937cb592d22f8e04054050eea9fc2e06897d98b19c885fb9696f67bbd

Aliases

arxiv: 2605.17688 · arxiv_version: 2605.17688v1 · doi: 10.48550/arxiv.2605.17688 · pith_short_12: CAIPD2JXZNMS · pith_short_16: CAIPD2JXZNMS2IXY · pith_short_8: CAIPD2JX

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CAIPD2JXZNMS2IXY4BAFIBIO5K \
  | 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: 1010f1e937cb592d22f8e04054050eea9fc2e06897d98b19c885fb9696f67bbd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02b6bc7c6900ec6ae621a5ea23e760c444af593603b80e707066eafb3e1360ac",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-17T23:01:40Z",
    "title_canon_sha256": "4608b235a496bee67eac0e47066a823d68de1702c5390cdea5e71017a375ca14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17688",
    "kind": "arxiv",
    "version": 1
  }
}