{"paper":{"title":"Pseudo-Calabi Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Kai Zheng, Xiuxiong Chen","submitted_at":"2010-04-15T16:22:05Z","abstract_excerpt":"We first define Pseudo-Calabi flow, as {equation*}\n  {{aligned}{{\\partial \\varphi}\\over {\\partial t}}&= -f(\\varphi), \\triangle_varphi f(\\varphi) &= S(\\varphi) - \\ul S.{aligned}. \\end{equation*} Then we prove the well-posedness of this flow including the short time existence, the regularity of the solution and the continuous dependence on the initial data. Next, we point out that the $L^\\infty$ bound on Ricci curvature is an obstruction to the extension of the pseudo-Calabi flow. Finally, we show that if there is a cscK metric in its K\\\"ahler class, then for any initial potential in a small $C^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2663","kind":"arxiv","version":3},"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"}