{"paper":{"title":"Some results on evolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Giuseppe Tomassini","submitted_at":"2012-01-11T12:01:42Z","abstract_excerpt":"Let $K$ be a compact subset of $\\mathbb C^n$, $K^\\ast K$ a closed subset. In this paper we are dealing with evolution $E_t(K,K^\\ast)$ of $K$ with fixed part $K^\\ast$ by Levi form. This amounts to solve a parabolic problem for an elliptic operator. We prove existence and unicity for such a problem and the solution $u(z,t)$ exists for any time $t\\ge 0$.If $K$ is a smooth graph $\\Gamma$ and $K^\\ast={\\rm b}\\Gamma$ the the evolution $E_t(\\Gamma,{\\rm b}\\Gamma)$ is still a graph. In particular, if ${\\rm b}\\Gamma$ bounds a Levi flat hypersurface $M$ then $E_t(\\Gamma,{\\rm b}\\Gamma)\\to M$ as $t\\to+\\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2287","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"}