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For $\\Lambda\\geq0$ and $\\gamma \\geq 0$ let $\\Omega_{\\Lambda, \\gamma}(\\mathcal{A})$ denote any extremal set of the shape optimization problem $$\n  \\sup\\{ \\mathrm{Tr}(-\\Delta_\\Omega-\\Lambda)_-^\\gamma: \\Omega \\in \\mathcal{A}, |\\Omega|=1\\}, $$ where $\\mathcal{A}$ is an admissible family of convex domains in $\\mathbb{R}^n$. If $\\gamma \\geq 1$ and $\\{\\Lambda_j\\}_{j\\geq1}$ is a positive sequence tending to infinity we prove that $\\{\\Omega_{\\Lambda_j, \\gamma}(\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.05680","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-11-17T13:55:06Z","cross_cats_sorted":["math.AP","math.OC"],"title_canon_sha256":"e9ad3ef721235222e5557a738b216362af711b7ef54fc3e380a31ae1d27274ed","abstract_canon_sha256":"a1bb0ac2a6ff53fd5f240e3c7ed30b9e8767250389f4279224d528cccf9c4288"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:14:21.555132Z","signature_b64":"vvBfm7XhkB4FtKTOZ6MAnqtoF53UwunG+q+4lg13KUD0AybfaYkvIaokpy9arPPQoFiW+3+IbTXMqYlzf9tTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd388acc36a85c4dd2ce3c5c2d4f1ef4992dd118e2e2c81690e93ff37fd58683","last_reissued_at":"2026-07-05T04:14:21.554753Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:14:21.554753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.OC"],"primary_cat":"math.SP","authors_text":"Simon Larson","submitted_at":"2016-11-17T13:55:06Z","abstract_excerpt":"For $\\Omega \\subset \\mathbb{R}^n$, a convex and bounded domain, we study the spectrum of $-\\Delta_\\Omega$ the Dirichlet Laplacian on $\\Omega$. 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