{"paper":{"title":"Relative K-stability and Extremal Sasaki metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Charles P. Boyer, Craig van Coevering","submitted_at":"2016-08-22T14:50:26Z","abstract_excerpt":"We define K-stability of a polarized Sasakian manifold relative to a maximal torus of automorphisms. The existence of a Sasaki-extremal metric in the polarization is shown to imply that the polarization is K-semistable. Computing this invariant for the deformation to the normal cone gives an extention of the Lichnerowicz obstruction, due to Gauntlett, Martelli, Sparks, and Yau, to an obstruction of Sasaki-extremal metrics. We use this to give a list of examples of Sasakian manifolds whose Sasaki cone contains no extremal representatives. These give the first examples of Sasaki cones of dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06184","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"}