{"paper":{"title":"Large Conformal metrics with prescribed sign-changing Gauss curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Carlos Rom\\'an, Manuel del Pino","submitted_at":"2014-07-08T00:23:01Z","abstract_excerpt":"Let $(M,g)$ be a two dimensional compact Riemannian manifold of genus $g(M)>1$. Let $f$ be a smooth function on $M$ such that $$f \\ge 0, \\quad f\\not\\equiv 0, \\quad \\min_M f = 0. $$ Let $p_1,\\ldots,p_n$ be any set of points at which $f(p_i)=0$ and $D^2f(p_i)$ is non-singular. We prove that for all sufficiently small $\\lambda>0$\n  there exists a family of \"bubbling\" conformal metrics $g_\\lambda=e^{u_\\lambda}g$ such that their Gauss curvature is given by the sign-changing function $K_{g_\\lambda}=-f+\\lambda^2$. Moreover, the family $u_\\lambda$ satisfies $$u_\\lambda(p_j) = -4\\log\\lambda -2\\log \\lef"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1912","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"}