{"paper":{"title":"Expanding curves in $\\mathrm{T}^1(\\mathbb{H}^n)$ under geodesic flow and equidistribution in homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lei Yang","submitted_at":"2013-03-25T03:52:41Z","abstract_excerpt":"Let $H = \\mathrm{SO}(n,1)$ and $A =\\{a(t) : t \\in \\mathbb{R}\\}$ be a maximal $\\mathbb{R}$-split Cartan subgroup of $H$. Let $G$ be a Lie group containing $H$ and $\\Gamma$ be a lattice of $G$. Let $x = g\\Gamma \\in G/\\Gamma$ be a point of $G/\\Gamma$ such that its $H$-orbit $Hx$ is dense in $G/\\Gamma$.\n  Let $\\phi: I= [a,b] \\rightarrow H$ be an analytic curve, then $\\phi(I)x$ gives an analytic curve in $G/\\Gamma$. In this article, we will prove the following result: if $\\phi(I)$ satisfies some explicit geometric condition, then $a(t)\\phi(I)x$ tends to be equidistributed in $G/\\Gamma$ as $t \\right"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6023","kind":"arxiv","version":2},"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"}