{"paper":{"title":"Isometric immersions and self-similar buckling in Non-Euclidean elastic sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","nlin.PS"],"primary_cat":"cond-mat.soft","authors_text":"Eran Sharon, John Gemmer, Shankar Venkataramani","submitted_at":"2015-04-03T03:29:36Z","abstract_excerpt":"The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian metrics. With this motivation we study the isometric immersion problem in strip and disk geometries. By finding explicit piecewise smooth solutions of hyperbolic Monge-Ampere equations on a strip, we show there exist periodic isometric immersions of hyperbolic surfaces in the small slope regime. We extend these solutions to exact isometric immersions through "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00738","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"}