{"paper":{"title":"Metric methods for heteroclinic connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Antonin Monteil, Filippo Santambrogio","submitted_at":"2016-02-17T17:11:16Z","abstract_excerpt":"We consider the problem $\\min\\int_{\\mathbb{R}} \\frac{1}{2}|\\dot{\\gamma}|^2+W(\\gamma)\\mathop{}\\mathopen{}\\mathrm{d} t $ among curves connecting two given wells of $W\\geq 0$ and we reduce it, following a standard method, to a geodesic problem of the form $\\min\\int_0^1 K(\\gamma)|\\dot{\\gamma}|\\mathop{}\\mathopen{}\\mathrm{d} t$ with $K=\\sqrt{2W}$. We then prove existence of curves minimizing this new action just by proving that the distance induced by $K$ is proper (i.e. its closed balls are compact). The assumptions on $W$ are minimal, and the method seems robust enough to be applied in the future "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05487","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"}