{"paper":{"title":"Prescribing Gaussian curvature on closed Riemann surface with conical singularity in the negative case","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Xiaobao Zhu, Yunyan Yang","submitted_at":"2017-06-07T06:50:23Z","abstract_excerpt":"The problem of prescribing Gaussian curvature on Riemann surface with conical singularity is considered. Let $(\\Sigma,\\beta)$ be a closed Riemann surface with a divisor $\\beta$, and $K_\\lambda=K+\\lambda$, where $K:\\Sigma\\rightarrow\\mathbb{R}$ is a H\\\"older continuous function satisfying $\\max_\\Sigma K= 0$, $K\\not\\equiv 0$, and $\\lambda\\in\\mathbb{R}$. If the Euler characteristic $\\chi(\\Sigma,\\beta)$ is negative, then by a variational method, it is proved that there exists a constant $\\lambda^\\ast>0$ such that for any $\\lambda\\leq 0$, there is a unique conformal metric with the Gaussian curvatur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02059","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"}