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In this paper we compute the spectra of their Laplace and Jacobi operators in terms of eigenvalues of second order Hill's equations.\n  For the minimal rotational examples, we prove that the stability index --the numbers of negative eigenvalues of the Jacobi operator counted with multiplicity -- is greater than $3 n+"},"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":"1902.07348","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-02-19T23:47:22Z","cross_cats_sorted":[],"title_canon_sha256":"e575e80f70f37d3db8d5f0ea48d58d0d87e42f43a0a1bd817e8a699987ae0301","abstract_canon_sha256":"6ceb13bc8c7371489e6f164b824a60cb2f6fef2abd7b8efa717bd1bf3e5bc89f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:44.532897Z","signature_b64":"e/aryRPlL2RMErD6ZD4jOMZXnSQEz8Grv9zOhIP2Pt3DBHU8VcKMqweFwMNwqDoFN0ZPavwac0LjsHaQLizGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3480562276a898510dea0adcb399e8c3f119a5f3d0c52cf91418f8f6078fad3b","last_reissued_at":"2026-05-17T23:50:44.532450Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:44.532450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectrum of the Laplacian and the Jacobi operator on rotational cmc hypersurfaces of spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Oscar Perdomo","submitted_at":"2019-02-19T23:47:22Z","abstract_excerpt":"Let $M\\subset \\mathbb{S}^{n+1}\\subset\\mathbb{R}^{n+2}$ be a compact cmc rotational hypersurface of the $(n+1)$-dimensional Euclidean unit sphere. Denote by $|A|^2$ the square of the norm of the second fundamental form and $J(f)=-\\Delta f-nf-|A|^2f$ the stability or Jacobi operator. 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