{"paper":{"title":"An obstacle problem for conical deformations of thin elastic sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Connor Mooney","submitted_at":"2017-07-10T16:42:59Z","abstract_excerpt":"A developable cone (\"d-cone\") is the shape made by an elastic sheet when it is pressed at its center into a hollow cylinder by a distance $\\epsilon$. Starting from a nonlinear model depending on the thickness $h > 0$ of the sheet, we prove a $\\Gamma$-convergence result as $h \\rightarrow 0$ to a fourth-order obstacle problem for curves in $\\mathbb{S}^2$. We then describe the exact shape of minimizers of the limit problem when $\\epsilon$ is small. In particular, we rigorously justify previous results in the physics literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02940","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"}