Pith Number

pith:7EHRGU3E

pith:2026:7EHRGU3EA3TENOAX2BCKFP3RIR

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The Dual Minkowski Problem under Group Actions

Junjie Shan

The dual Minkowski problem has a complete existence characterization for G-invariant convex bodies when measures concentrate properly on invariant subspaces.

arxiv:2605.15891 v1 · 2026-05-15 · math.MG

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Claims

C1strongest claim

For 0<q≤n, we give a complete existence characterization in the framework of G-invariant convex bodies, recovering the origin-symmetric setting when G={±I}. The necessary and sufficient conditions concern the concentration of the measure on G-invariant subspaces, both in the range 0<q<n and at the critical endpoint q=n.

C2weakest assumption

The given measure must obey specific concentration restrictions on the G-invariant subspaces; if this concentration condition fails, no G-invariant solution exists, as this forms the necessary and sufficient criterion stated for both the subcritical and critical cases.

C3one line summary

The paper establishes necessary and sufficient conditions for the existence of G-invariant convex bodies solving the dual Minkowski problem, with the conditions depending on measure concentration on G-invariant subspaces, including the logarithmic case at q = n.

References

46 extracted · 46 resolved · 0 Pith anchors

[1] B¨ or¨ oczky, E 2013

[2] B¨ or¨ oczky, F 2019

[3] B¨ or¨ oczky, P 2016

[4] B¨ or¨ oczky, M 2016

[5] B¨ or¨ oczky, M 2018

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:23.986223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f90f13536406e646b817d044a2bf714455c94fc1e31a769291852e313cad7cd6

Aliases

arxiv: 2605.15891 · arxiv_version: 2605.15891v1 · doi: 10.48550/arxiv.2605.15891 · pith_short_12: 7EHRGU3EA3TE · pith_short_16: 7EHRGU3EA3TENOAX · pith_short_8: 7EHRGU3E

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/7EHRGU3EA3TENOAX2BCKFP3RIR \
  | 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: f90f13536406e646b817d044a2bf714455c94fc1e31a769291852e313cad7cd6

Canonical record JSON

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    "abstract_canon_sha256": "80f369f55965a7141f43a9b6a891135af82eeb233b691fc8c51dca0278306ca1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-05-15T12:21:59Z",
    "title_canon_sha256": "b324d359802272decb4005d00675ca97431d67ea38dd7752b42b586bf4c37221"
  },
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}