{"paper":{"title":"Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ionel-Dumitrel Ghiba, Jendrik Voss, Macro Valerio d'Agostino, Patrizio Neff, Robert J. Martin","submitted_at":"2026-08-07T10:39:36Z","abstract_excerpt":"Motivated by classical constitutive inequalities in isotropic nonlinear elasticity theory, we investigate the monotonicity of isotropic tensor functions of the form\n  \\[\n  \\Sigma_f\\colon\\mathrm{Sym}(n)\\to\\mathrm{Sym}(n)\\,,\\quad \\Sigma_f(Q^T\\mathrm{diag}(\\lambda_1,\\dotsc,\\lambda_n)\\, Q) = Q^T\\mathrm{diag}(f(\\lambda_1,\\dotsc,\\lambda_n))\\, Q \\quad\\forall\\;Q\\in\\mathrm{O}(n)\n  \\]\n  with a vector function $f=(f_1,\\dotsc,f_n)\\colon\\mathbb{R}^n\\to\\mathbb{R}^n$ which is symmetric, i.e.\\ satisfies\n  \\[\n  f_i(\\lambda_{\\pi(1)},\\dotsc,\\lambda_{\\pi(n)}) = f_{\\pi(i)}(\\lambda_1,\\dotsc,\\lambda_n)\n  \\]\n  for an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07087","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.07087/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}