{"paper":{"title":"Uniform ball property and existence of optimal shapes for a wide class of geometric functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.OC","authors_text":"Jeremy Dalphin (IECL)","submitted_at":"2015-04-16T11:33:51Z","abstract_excerpt":"In this paper, we are interested in shape optimization problems involving the ge ometry (normal, curvatures) of the surfaces. We consider a class of hypersurface s in $\\mathbb{R}^{n}$ satisfying a uniform ball condition and we prove the exist ence of a $C^{1,1}$-regular minimizer for general geometric functionals and cons traints involving the first- and second-order properties of surfaces, such as in $\\mathbb{R}^{3}$ problems of the form:\n  $$ \\inf \\int_{\\partial \\Omega} j_0 [ \\mathbf{x},\\mathbf{n}(\\mathbf{x}) ] dA (\\mathbf{x}) + \\int_{\\partial \\Omega} j_1 [ \\mathbf{x},\\mathbf{n}(\\mathbf{x}),"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04189","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"}