{"paper":{"title":"Gauge rigidity in an inverse problem for the prescribed Gaussian curvature equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yi-Hsuan Lin","submitted_at":"2026-07-06T04:26:11Z","abstract_excerpt":"We prove a uniqueness result for an inverse boundary problem associated with the prescribed Gaussian curvature equation\n  \\[\n  \\det D^2u=K(x)(1+|\\nabla u|^2)^2\n  \\]\n  for graphs over a planar domain. The comparison is made on a common open class of smooth boundary values for which both admissible Dirichlet problems are well posed. We show that, if the corresponding nonlinear Dirichlet-to-Neumann maps agree on this class and the two prescribed curvatures have the same first boundary jet, then the curvatures agree in the whole domain.\n  The main difficulty comes from a gauge obstruction already "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04657","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/2607.04657/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"}