{"paper":{"title":"Nonexistence of extremals for an inequality of Adimurthi-Druet on a closed Riemann surface","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Yunyan Yang","submitted_at":"2018-12-14T12:37:33Z","abstract_excerpt":"Based on a recent work of Mancini-Thizy [28], we obtain the nonexistence of extremals for an inequality of Adimurthi-Druet [1] on a closed Riemann surface $(\\Sigma,g)$. Precisely, if $\\lambda_1(\\Sigma)$ is the first eigenvalue of the Laplace-Beltrami operator with respect to the zero mean value condition, then there exists a positive real number $\\alpha^\\ast<\\lambda_1(\\Sigma)$ such that for all $\\alpha\\in (\\alpha^\\ast,\\lambda_1(\\Sigma))$, the supremum $$\\sup_{u\\in W^{1,2}(\\Sigma,g),\\,\\int_\\Sigma udv_g=0,\\,\\|\\nabla_gu\\|_2\\leq 1}\\int_\\Sigma \\exp(4\\pi u^2(1+\\alpha\\|u\\|_2^2))dv_g$$\n  can not be at"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05884","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"}