{"paper":{"title":"Bubbling solutions for Moser-Trudinger type equations on compact Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Monica Musso, Pablo Figueroa","submitted_at":"2017-09-04T18:20:28Z","abstract_excerpt":"We study an elliptic equation related to the Moser-Trudinger inequality on a compact Riemann surface $(S,g)$, $$ \\Delta_g u+\\lambda \\Biggl(ue^{u^2}-{1\\over |S|} \\int_S ue^{u^2} dv_g\\Biggl)=0,\\quad\\text{in $S$},\\qquad \\int_S u\\,dv_g=0, $$ where $\\lambda>0$ is a small parameter, $|S|$ is the area of $S$, $\\Delta_g$ is the Laplace-Beltrami operator and $dv_g$ is the area element. Given any integer $k\\geq 1$, under general conditions on $S$ we find a bubbling solution $u_\\lambda$ which blows up at exactly $k$ points in $S$, as $\\lambda \\to0$. When $S$ is a flat two-torus in rectangular form, we fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01106","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"}