{"paper":{"title":"Estimates of the Green function and the initial-Dirichlet problem for the heat equation in sub-Riemannian spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Isidro H. Munive, Nicola Garofalo","submitted_at":"2016-03-09T18:20:13Z","abstract_excerpt":"In a cylinder $D_T = \\Omega \\times (0,T)$, where $\\Omega\\subset \\mathbb{R}^n$, we examine the relation between the $L$-caloric measure, $d\\omega^{(x,t)}$, where $L$ is the heat operator associated with a system of vector fields of H\\\"ormander type, and the measure $d\\sigma_X\\times dt$, where $d\\sigma_X$ is the intrinsic $X$-perimeter measure. The latter constitutes the appropriate replacement for the standard surface measure on the boundary and plays a central role in sub-Riemannian geometric measure theory. Under suitable assumptions on the domain $\\Omega$ we establish the mutual absolute con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02988","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"}