{"paper":{"title":"Complex-ellipticity, dimensional estimates and plane wave rigidity in $BV^{\\mathbb A}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adolfo Arroyo-Rabasa","submitted_at":"2026-06-10T13:28:51Z","abstract_excerpt":"We characterize complex-elliptic operators $\\mathbb A(D)$ through a hierarchy of overdeterminacy ($\\ell$-vanishing) quantifying the structural twisting of their symbols. This framework yields the optimal dimensional estimate for $BV^{\\mathbb A}$-functions: a measure ${\\mathbb A} u$ cannot concentrate on sets of dimension below $n-1$. Consequently, the jump part of ${\\mathbb A} u$ is characterized as an $(n-1)$-dimensional surface measure with density given by the symbol and the two-sided traces. Building on this dimensional bound, we prove that measures satisfying $\\frac{{\\mathbb A} u}{|{\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12061","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/2606.12061/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"}