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If $p \\ge 2n-1$, then among hypersurfaces in $\\mathbb{R}^{2n}$ which are $O(n) \\times O(n)$-invariant and have one fixed boundary component, there is a surface which maximizes the first Dirichlet eigenvalue of the $p$-Laplacian. This surface is either Simons' cone or a $C^1$ hypersurface, depending on $p$ and $n$. If $n$ is fixed and $p$ is large, then the maximizing surface is not Simons' cone. If $p=2$ and $n \\le 5$, then Simons' cone does not ma"},"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":"1601.00999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-05T22:15:56Z","cross_cats_sorted":["math.DG","math.SP"],"title_canon_sha256":"b51081615e8cea7a27652f0a1e358a1e40477bd069b6f342197485292f2ad5fa","abstract_canon_sha256":"c64abed7b988ca2142218b49899f92176e7802663301c7c17618d90e04c15e88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:46.010059Z","signature_b64":"+CHWjP0GOIROLFOKlv0KT4hPqI3dNjzjIZ1woN5Aktr3TvDgGOetu9xBZD+9wsbz3AeUUbhCHx+Rsm4x6bXkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7102ccf3d0ec8feacfdee12db16294569fb42a3220e814f7f733df93882f02ce","last_reissued_at":"2026-05-18T01:00:46.009662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:46.009662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simons' cone and equivariant maximization of the first $p$-Laplace eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Sinan Ariturk","submitted_at":"2016-01-05T22:15:56Z","abstract_excerpt":"We consider an optimization problem for the first Dirichlet eigenvalue of the $p$-Laplacian on a hypersurface in $\\mathbb{R}^{2n}$, with $n \\ge 2$. If $p \\ge 2n-1$, then among hypersurfaces in $\\mathbb{R}^{2n}$ which are $O(n) \\times O(n)$-invariant and have one fixed boundary component, there is a surface which maximizes the first Dirichlet eigenvalue of the $p$-Laplacian. This surface is either Simons' cone or a $C^1$ hypersurface, depending on $p$ and $n$. If $n$ is fixed and $p$ is large, then the maximizing surface is not Simons' cone. 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