{"paper":{"title":"Improved Moser-Trudinger type inequalities in the hyperbolic space $\\mathbb H^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Van Hoang Nguyen","submitted_at":"2017-09-27T16:31:04Z","abstract_excerpt":"We establish an improved version of the Moser-Trudinger inequality in the hyperbolic space $\\mathbb H^n$, $n\\geq 2$. Namely, we prove the following result: for any $0 \\leq \\lambda < \\left(\\frac{n-1}n\\right)^n$, then we have $$ \\sup_{\\substack{u\\in C_0^\\infty(\\mathbb H^n) \\int_{\\mathbb H^n} |\\nabla_g u|_g^n d\\text{Vol}_g -\\lambda \\int_{\\mathbb H^n} |u|^n d\\text{ Vol}_g \\leq 1}} \\int_{\\mathbb H^n} \\Phi_n(\\alpha_n |u|^{\\frac{n}{n-1}}) d\\text{ Vol}_g < \\infty, $$ where $\\alpha_n = n \\omega_{n-1}^{\\frac1{n-1}}$, $\\omega_{n-1}$ denotes the surface area of the unit sphere in $\\mathbb R^n$ and $\\Phi_n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09608","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"}