{"paper":{"title":"The inverse curve shortening flow on the hyperbolic plane","license":"http://creativecommons.org/licenses/by/4.0/","headline":"In the hyperbolic plane, all parabolic solitons of the inverse curve shortening flow are graphs over the y-axis and all conformal solitons are graphs over the x-axis in the upper half-plane model.","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ivan Krznari\\'c, Rafael L\\'opez","submitted_at":"2026-05-14T05:07:35Z","abstract_excerpt":"We study the inverse curve shortening flow in the hyperbolic plane $\\h^2$. We classify all solitons with respect to parabolic and conformal vector fields of $\\h^2$. In the upper half-plane model of $\\h^2$, we prove that parabolic solitons are all graphs on the $y$-axis, whereas conformal solitons are graphs on the $x$-axis. We study the concavity of these solitons and when they approach the coordinate axes."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We classify all solitons with respect to parabolic and conformal vector fields of H^2. In the upper half-plane model of H^2, we prove that parabolic solitons are all graphs on the y-axis, whereas conformal solitons are graphs on the x-axis.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The flow is assumed to be well-defined for the curves considered, and the vector fields are taken to be parabolic or conformal without further justification of why these are the only relevant cases for soliton classification.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Solitons for the inverse curve shortening flow on H^2 are classified as graphs over the coordinate axes in the upper half-plane model, with analysis of their concavity and asymptotic behavior.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In the hyperbolic plane, all parabolic solitons of the inverse curve shortening flow are graphs over the y-axis and all conformal solitons are graphs over the x-axis in the upper half-plane model.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6198090b7e328ef93eb72201f6915df4be1d1820410cdddea825a88e035fb777"},"source":{"id":"2605.14385","kind":"arxiv","version":1},"verdict":{"id":"79b274b2-7b3d-43d0-b3db-6273414a850a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:42:08.170194Z","strongest_claim":"We classify all solitons with respect to parabolic and conformal vector fields of H^2. In the upper half-plane model of H^2, we prove that parabolic solitons are all graphs on the y-axis, whereas conformal solitons are graphs on the x-axis.","one_line_summary":"Solitons for the inverse curve shortening flow on H^2 are classified as graphs over the coordinate axes in the upper half-plane model, with analysis of their concavity and asymptotic behavior.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The flow is assumed to be well-defined for the curves considered, and the vector fields are taken to be parabolic or conformal without further justification of why these are the only relevant cases for soliton classification.","pith_extraction_headline":"In the hyperbolic plane, all parabolic solitons of the inverse curve shortening flow are graphs over the y-axis and all conformal solitons are graphs over the x-axis in the upper half-plane model."},"references":{"count":22,"sample":[{"doi":"","year":2016,"title":"B. D. Allen, Non-compact solutions to inverse mean curvature flow in hyperbolic space. Ph.D. thesis, University of Tennessee, Knoxville, 2016","work_id":"e644f30d-accc-4bf6-a467-1e8a4eaec66d","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"A. Bueno, R. L´ opez, Horo-shrinkers in the hyperbolic space. Taiwanese J. Math. 29 (2025), 1037–1059","work_id":"5b61f112-cabf-4f0f-98dd-97523b2b2821","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"A. Bueno, R. L´ opez, The class of grim reapers inH 2 ×R. J. Math. Anal. Appl. 541 (2025), 128730","work_id":"dfe20f32-6e8e-4fd5-a989-11fb588d3465","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"I. Castro, A. M. Lerma, Lagrangian homothetic solitons for the inverse mean curvature flow. Results Math. 71 (2017), 3–4","work_id":"2ce826c4-23a1-4d2e-91d0-2138626ec6ed","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"B. Choi, P. Daskalopoulos, Evolution of non-compact hypersurfaces by inverse mean curvature. Duke Math. J. 170 (2021), 2755–2803","work_id":"3224e0ee-ff68-423e-ba0b-225539ff969c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":22,"snapshot_sha256":"a71ae36b3c2dfe0e31fa37876c61ac704813ab122cae441540b889986bb18667","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"}