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Assume Ricc_g\\geq (1-n)B^2, and either p>2 and Sec_g(x)=o(dist^2(x,a)) when dist^2(x,a)\\to\\infty for a\\in M, or 1<p<2 and Sec_g(x)\\leq 0. If q>p-1> 0, any C^1 solution of (E) -\\Gd_pu+\\abs{\\nabla u}^q=0 on M satisfies \\abs{\\nabla u(x)}\\leq c_{n,p,q}B^{\\frac{1}{q+1-p}} for some constant c_{n,p,q}>0. As a consequence there exists c_{n,p}>0 such that any positive p-harmonic function v on M satisfies v(a)e^{-c_{n,p}B\\dist (x,a)}\\leq v(x)\\leq v(a)e^{c_{n,p}B"},"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":"1305.6720","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-29T08:37:55Z","cross_cats_sorted":[],"title_canon_sha256":"3f6a513b78d20c0d107c1192e4349368fd90c628dfbff7ee1b1c43f1f78350ed","abstract_canon_sha256":"3671beb70f16e29cf0b5257266919765ae1bf333b753228c4bb030e1e5c2a015"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:45.025400Z","signature_b64":"CxClz/i457rhOlAN/hCuuVeXRNcnpDOGii5T3LLBMD0zoE6JP4ypeyoDhb4hwr4Yv0Qpa3SM8q7BHLZVB9FlAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e5e1578de35bf15547cb45e797405b37a55132d40f5f7db17ff7852c25df283","last_reissued_at":"2026-05-18T03:21:45.024834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:45.024834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasilinear elliptic Hamilton-Jacobi equations on complete manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laurent Veron (LMPT), Marie-Fran\\c{c}oise Bidaut-Veron (LMPT), Marta Garcia-Huidobro","submitted_at":"2013-05-29T08:37:55Z","abstract_excerpt":"Let (M^n,g) be a n-dimensional complete, non-compact and connected Riemannian manifold, with Ricci tensor Ricc_g and sectional curvature Sec_g. Assume Ricc_g\\geq (1-n)B^2, and either p>2 and Sec_g(x)=o(dist^2(x,a)) when dist^2(x,a)\\to\\infty for a\\in M, or 1<p<2 and Sec_g(x)\\leq 0. If q>p-1> 0, any C^1 solution of (E) -\\Gd_pu+\\abs{\\nabla u}^q=0 on M satisfies \\abs{\\nabla u(x)}\\leq c_{n,p,q}B^{\\frac{1}{q+1-p}} for some constant c_{n,p,q}>0. As a consequence there exists c_{n,p}>0 such that any positive p-harmonic function v on M satisfies v(a)e^{-c_{n,p}B\\dist (x,a)}\\leq v(x)\\leq v(a)e^{c_{n,p}B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6720","kind":"arxiv","version":2},"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":"1305.6720","created_at":"2026-05-18T03:21:45.024944+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.6720v2","created_at":"2026-05-18T03:21:45.024944+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6720","created_at":"2026-05-18T03:21:45.024944+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZPBK6G6GW7R","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZPBK6G6GW7RKVD4","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZPBK6G6","created_at":"2026-05-18T12:27:45.050594+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/FZPBK6G6GW7RKVD4WRPHS5AFWN","json":"https://pith.science/pith/FZPBK6G6GW7RKVD4WRPHS5AFWN.json","graph_json":"https://pith.science/api/pith-number/FZPBK6G6GW7RKVD4WRPHS5AFWN/graph.json","events_json":"https://pith.science/api/pith-number/FZPBK6G6GW7RKVD4WRPHS5AFWN/events.json","paper":"https://pith.science/paper/FZPBK6G6"},"agent_actions":{"view_html":"https://pith.science/pith/FZPBK6G6GW7RKVD4WRPHS5AFWN","download_json":"https://pith.science/pith/FZPBK6G6GW7RKVD4WRPHS5AFWN.json","view_paper":"https://pith.science/paper/FZPBK6G6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.6720&json=true","fetch_graph":"https://pith.science/api/pith-number/FZPBK6G6GW7RKVD4WRPHS5AFWN/graph.json","fetch_events":"https://pith.science/api/pith-number/FZPBK6G6GW7RKVD4WRPHS5AFWN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZPBK6G6GW7RKVD4WRPHS5AFWN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZPBK6G6GW7RKVD4WRPHS5AFWN/action/storage_attestation","attest_author":"https://pith.science/pith/FZPBK6G6GW7RKVD4WRPHS5AFWN/action/author_attestation","sign_citation":"https://pith.science/pith/FZPBK6G6GW7RKVD4WRPHS5AFWN/action/citation_signature","submit_replication":"https://pith.science/pith/FZPBK6G6GW7RKVD4WRPHS5AFWN/action/replication_record"}},"created_at":"2026-05-18T03:21:45.024944+00:00","updated_at":"2026-05-18T03:21:45.024944+00:00"}