{"paper":{"title":"The inverse Monge-Ampere flow and applications to Kahler-Einstein metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Ryosuke Takahashi, Tomoyuki Hisamoto, Tristan C. Collins","submitted_at":"2017-12-05T15:04:17Z","abstract_excerpt":"We introduce the inverse Monge-Ampere flow as the gradient flow of the Ding energy functional on the space of Kahler metrics in $2 \\pi \\lambda c_1(X)$ for $\\lambda=\\pm 1$. We prove the long-time existence of the flow. In the canonically polarized case, we show that the flow converges smoothly to the unique Kahler-Einstein metric with negative Ricci curvature. In the Fano case, assuming $X$ admits a Kahler-Einstein metric, we prove the weak convergence of the flow to a Kahler-Einstein metric. In general, we expect that the limit of the flow is related with the optimally destabilizing test confi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01685","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"}