{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:N3ZLT64AGSUGGBELXD6WUFCNGX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cf5385bfb5a21c5c84ba09441df7ecb5e8025dc88ba0542d10442620426f870a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-01T17:06:07Z","title_canon_sha256":"6807d26213cc2b839745dee9ad638b797217f2eb9844ff9b492d55c648982d39"},"schema_version":"1.0","source":{"id":"1202.0218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0218","created_at":"2026-05-18T04:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0218v1","created_at":"2026-05-18T04:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0218","created_at":"2026-05-18T04:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"N3ZLT64AGSUG","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N3ZLT64AGSUGGBEL","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N3ZLT64A","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:895ee47d658afb12f45cc3d6cc0cb9bb06cf8df7553841b0d3febfa0d7eb875d","target":"graph","created_at":"2026-05-18T04:03:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the asymptotic behavior of the nonlinear parabolic flows $u_{t}=F(D^2 u^m)$ when $t\\ra \\infty$ for $m\\geq 1$, and the geometric properties for solutions of the following elliptic nonlinear eigenvalue problems:\n  F(D^2 \\vp) &+ \\mu\\vp^{p}=0, \\quad \\vp>0\\quad\\text{in $\\Omega$}\n  \\vp&=0\\quad\\text{on $\\p\\Omega$}\nposed in a (strictly) convex and smooth domain $\\Omega\\subset\\re^n$ for $0< p \\leq 1,$ where $F(\\cdot)$ is uniformly elliptic, positively homogeneous of order one and concave. We establish that $\\log (\\vp)$ is concave in the case $p=1$ and that the function $\\vp^{\\frac{1-p}{2}}$ is","authors_text":"Ki-Ahm Lee, Soojung Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-01T17:06:07Z","title":"Asymptotic Behavior in Degenerate Parabolic Fully Nonlinear equations and its application to Elliptic Eigenvalue Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0218","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:699d1a6f913d315cee3263e09d333d87835c287ff7389f493bb11334092308d9","target":"record","created_at":"2026-05-18T04:03:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cf5385bfb5a21c5c84ba09441df7ecb5e8025dc88ba0542d10442620426f870a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-01T17:06:07Z","title_canon_sha256":"6807d26213cc2b839745dee9ad638b797217f2eb9844ff9b492d55c648982d39"},"schema_version":"1.0","source":{"id":"1202.0218","kind":"arxiv","version":1}},"canonical_sha256":"6ef2b9fb8034a863048bb8fd6a144d35f8cf439d43d9edf059f72b3579fa60cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ef2b9fb8034a863048bb8fd6a144d35f8cf439d43d9edf059f72b3579fa60cc","first_computed_at":"2026-05-18T04:03:19.861010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:19.861010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V8wIuzBzio5vKdFf6Kt/AIf26YugyCwPG75Im4aDTkGCpH+K7o8vh6dRx0UcT4wZtmTu6wVnTDYXHCIrzGWaCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:19.861558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:699d1a6f913d315cee3263e09d333d87835c287ff7389f493bb11334092308d9","sha256:895ee47d658afb12f45cc3d6cc0cb9bb06cf8df7553841b0d3febfa0d7eb875d"],"state_sha256":"34885df7cfdc8ac7b3b6503b40190f82a58f2ca7ea7a4da7a1a58cd24b3bb9a6"}