{"paper":{"title":"Towards characterization of all $3\\times3$ extremal quasiconvex quadratic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.AG","authors_text":"Davit Harutyunyan, Graeme W. Milton","submitted_at":"2015-12-14T05:22:48Z","abstract_excerpt":"Given a $d\\times d$ quasiconvex quadratic form, $d\\geq 3,$ we prove that if the determinant of its acoustic tensor is an irreducible extremal polynomial that is not identically zero, then the form itself is an extremal quasiconvex quadratic form, i.e. it loses its quasiconvexity whenever a convex quadratic form is subtracted from it. In the special case $d=3,$ we slightly weaken the condition, namely we prove, that if the determinant of the acoustic tensor of the quadratic form is an extremal polynomial that is not a perfect square, then the form itself is an extremal quadratic form. In the ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04174","kind":"arxiv","version":3},"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"}