{"paper":{"title":"Harmonic determinants and unique continuation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Mihajlo Ceki\\'c","submitted_at":"2018-03-24T23:56:06Z","abstract_excerpt":"We give partial answers to the following question: if $F$ is an $m$ by $m$ matrix on $\\mathbb{R}^n$ satisfying a second order linear elliptic equation, does $\\det F$ satisfy the strong unique continuation property? We give counterexamples in the case when the operator is a general non-diagonal operator and also for some diagonal operators. Positive results are obtained when $n = 1$ and any $m$, when $n = 2$ for the Laplace-Beltrami operator and also twisted with a Yang-Mills connection. Reductions to special cases when $n = 2$ are obtained. The last section considers an application to the Cald"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09182","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"}