{"paper":{"title":"Shape Transitions in Hyperbolic Non-Euclidean Plates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"cond-mat.soft","authors_text":"John Gemmer, Shankar Venkataramani","submitted_at":"2012-08-31T23:27:37Z","abstract_excerpt":"We present and summarize the results of recent studies on non-Euclidean plates with imposed constant negative Gaussian curvature in both the F\\\"oppl - von K\\'arm\\'an and Kirchhoff approximations. Motivated by experimental results we focus on annuli with a periodic profile. We show that in the F\\\"oppl - von K\\'arm\\'an approximation there are only two types of global minimizers -- flat and saddle shaped deformations with localized regions of stretching near the boundary of the annulus. We also show that there exists local minimizers with $n$-waves that have regions of stretching near their lines"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0031","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"}