{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:6HMNOC43KC2CCEN2COKVO65SA2","short_pith_number":"pith:6HMNOC43","schema_version":"1.0","canonical_sha256":"f1d8d70b9b50b42111ba1395577bb206b0477b47f589584f719dad22f7356876","source":{"kind":"arxiv","id":"1907.10957","version":1},"attestation_state":"computed","paper":{"title":"Sharp Estimates for the Principal Eigenvalue of the p-Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Thomas Koerber","submitted_at":"2019-07-25T10:45:50Z","abstract_excerpt":"Given an elliptic diffusion operator $L$ defined on a compact and connected manifold (possibly with a convex boundary in a suitable sense) with an $L$-invariant measure $m$, we introduce the non-linear $p-$operator $L_p$, generalizing the notion of the $p-$Laplacian. Using techniques of the intrinsic $\\Gamma_2$-calculus, we prove the sharp estimate $\\lambda\\geq (p-1)\\pi_p^p/D^p$ for the principal eigenvalue of $L_p$ with Neumann boundary conditions under the assumption that $L$ satisfies the curvature-dimension condition BE$(0,N)$ for some $N\\in[1,\\infty)$. Here, $D$ denotes the intrinsic diam"},"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":"1907.10957","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-25T10:45:50Z","cross_cats_sorted":[],"title_canon_sha256":"d9b48c3d486b90835f5d1bf64d7715d0aedb09ced6585dbb8546de46817bba4d","abstract_canon_sha256":"8fd3b15e2635a5b73a0e3969f1abc2b39db195223b4c7f873a6c73476893f5cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:33.891838Z","signature_b64":"SzSifLhlMnSi3z6I6Vj7XzjSfU4aVPnYtN3gCXP38c7Chq2bloepQlQikhOHjRONifwLR5/VySdY5/xNhei8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1d8d70b9b50b42111ba1395577bb206b0477b47f589584f719dad22f7356876","last_reissued_at":"2026-05-17T23:39:33.891180Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:33.891180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Estimates for the Principal Eigenvalue of the p-Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Thomas Koerber","submitted_at":"2019-07-25T10:45:50Z","abstract_excerpt":"Given an elliptic diffusion operator $L$ defined on a compact and connected manifold (possibly with a convex boundary in a suitable sense) with an $L$-invariant measure $m$, we introduce the non-linear $p-$operator $L_p$, generalizing the notion of the $p-$Laplacian. Using techniques of the intrinsic $\\Gamma_2$-calculus, we prove the sharp estimate $\\lambda\\geq (p-1)\\pi_p^p/D^p$ for the principal eigenvalue of $L_p$ with Neumann boundary conditions under the assumption that $L$ satisfies the curvature-dimension condition BE$(0,N)$ for some $N\\in[1,\\infty)$. Here, $D$ denotes the intrinsic diam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10957","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.10957","created_at":"2026-05-17T23:39:33.891292+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.10957v1","created_at":"2026-05-17T23:39:33.891292+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10957","created_at":"2026-05-17T23:39:33.891292+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HMNOC43KC2C","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HMNOC43KC2CCEN2","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HMNOC43","created_at":"2026-05-18T12:33:10.108867+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6HMNOC43KC2CCEN2COKVO65SA2","json":"https://pith.science/pith/6HMNOC43KC2CCEN2COKVO65SA2.json","graph_json":"https://pith.science/api/pith-number/6HMNOC43KC2CCEN2COKVO65SA2/graph.json","events_json":"https://pith.science/api/pith-number/6HMNOC43KC2CCEN2COKVO65SA2/events.json","paper":"https://pith.science/paper/6HMNOC43"},"agent_actions":{"view_html":"https://pith.science/pith/6HMNOC43KC2CCEN2COKVO65SA2","download_json":"https://pith.science/pith/6HMNOC43KC2CCEN2COKVO65SA2.json","view_paper":"https://pith.science/paper/6HMNOC43","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.10957&json=true","fetch_graph":"https://pith.science/api/pith-number/6HMNOC43KC2CCEN2COKVO65SA2/graph.json","fetch_events":"https://pith.science/api/pith-number/6HMNOC43KC2CCEN2COKVO65SA2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HMNOC43KC2CCEN2COKVO65SA2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HMNOC43KC2CCEN2COKVO65SA2/action/storage_attestation","attest_author":"https://pith.science/pith/6HMNOC43KC2CCEN2COKVO65SA2/action/author_attestation","sign_citation":"https://pith.science/pith/6HMNOC43KC2CCEN2COKVO65SA2/action/citation_signature","submit_replication":"https://pith.science/pith/6HMNOC43KC2CCEN2COKVO65SA2/action/replication_record"}},"created_at":"2026-05-17T23:39:33.891292+00:00","updated_at":"2026-05-17T23:39:33.891292+00:00"}