Pith Number

pith:VCLAHK3I

pith:2026:VCLAHK3IJJSDQL3MNC7IG7FV4S

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A Brunn-Minkowski inequality for Schr\"odinger operators with Kato class potentials

Alessandro Carbotti

Schrödinger operators with convex Kato potentials obey a Brunn-Minkowski inequality on their first Dirichlet eigenvalue.

arxiv:2603.29989 v5 · 2026-03-31 · math.AP

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

In this paper we prove a Brunn-Minkowski inequality for the first Dirichlet eigenvalue of a Schrödinger type operator H_V := -div(A ∇) + V, where V is convex and Kato decomposable, using the trace class property of the generated semigroup.

C2weakest assumption

The potential V must be convex and Kato decomposable, and the semigroup generated by the operator must be trace class (and ultracontractive for the log-concavity conclusions).

C3one line summary

A Brunn-Minkowski inequality holds for the ground-state eigenvalue of Schrödinger operators with convex Kato decomposable potentials.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-07-10T01:18:59.296250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a89603ab684a64382f6c68be837cb5e49bfe138871e87b1ee685f4f37d1e64d6

Aliases

arxiv: 2603.29989 · arxiv_version: 2603.29989v5 · doi: 10.48550/arxiv.2603.29989 · pith_short_12: VCLAHK3IJJSD · pith_short_16: VCLAHK3IJJSDQL3M · pith_short_8: VCLAHK3I

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VCLAHK3IJJSDQL3MNC7IG7FV4S \
  | 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: a89603ab684a64382f6c68be837cb5e49bfe138871e87b1ee685f4f37d1e64d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e401e0d5e8b8c5580cc237ef23d56f65e789ff8bec83e1783d80b96bd4fee4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-03-31T16:54:27Z",
    "title_canon_sha256": "9a503e98d6bb01fb3a936eef33624ba0d94cfd260fc962fd4b48f4c6b78ef825"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.29989",
    "kind": "arxiv",
    "version": 5
  }
}