{"paper":{"title":"K\\\"ahler-Ricci flow of cusp singularities on quasi projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Albert Chau, Ka-Fai Li, Liangming Shen","submitted_at":"2017-08-09T04:53:28Z","abstract_excerpt":"Let $\\overline{M}$ be a compact complex manifold with smooth K\\\"ahler metric $\\eta$, and let $D$ be a smooth divisor on $\\overline{M}$. Let $M=\\overline{M}\\setminus D$ and let $\\hat{\\omega}$ be a Carlson-Griffiths type metric on $M$. We study complete solutions to K\\\"ahler-Ricci flow on $M$ which are comparable to $\\hat{\\omega}$, starting from a smooth initial metric $\\omega_0=\\eta +i\\partial \\bar{\\partial} \\phi_0$ where $\\phi_0\\in C^{\\infty}(M)$. When $\\omega_0\\geq c \\hat{\\omega}$ on $M$ for some $c>0$ and $\\phi_0$ has zero Lelong number, we construct a smooth solution $\\omega(t)$ to K\\\"ahler"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02717","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"}