{"paper":{"title":"A classification of isolated singularities of elliptic Monge-Amp\\`ere equations in dimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Asun Jim\\'enez, Jos\\'e A. G\\'alvez, Pablo Mira","submitted_at":"2012-10-19T09:42:35Z","abstract_excerpt":"Let $\\mathcal{M}_1$ denote the space of solutions $z(x,y)$ to an elliptic, real analytic Monge-Amp\\`ere equation ${\\rm det} (D^2 z)=\\varphi(x,y,z,Dz)>0$ whose graphs have a non-removable isolated singularity at the origin. We prove that $\\mathcal{M}_1$ is in one-to-one correspondence with $\\mathcal{M}_2\\times Z_2$, where $\\mathcal{M}_2$ is a suitable subset of the class of regular, real analytic strictly convex Jordan curves in $R^2$. We also describe the asymptotic behavior of solutions of the Monge-Amp\\`ere equation in the $C^k$-smooth case, and a general existence theorem for isolated singu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5362","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"}