{"paper":{"title":"The $\\Box_b$-heat equation on quadric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Albert Boggess, Andrew Raich","submitted_at":"2009-07-01T13:44:09Z","abstract_excerpt":"In this article, we give an explicit calculation of the partial Fourier transform of the $\\Box_b$-heat equation on quadric submanifolds of $M\\subset C^n\\times C^m$. As a consequence, we can also compute the heat kernel associated to the weighted dbar-equation in $C^n$ when the weight is given by $\\exp(-\\phi(z,z)\\cdot\\lambda)$ where $\\phi: C^n\\times C^n\\to C^m$ is a quadratic, sesquilinear form and $\\lambda\\in R^m$. Our method involves the representation theory of the Lie group $M$ and the group Fourier transform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0148","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"}