{"paper":{"title":"Asymptotic behavior of flows by powers of the Gaussian curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Kyeongsu Choi, Panagiota Daskalopoulos, Simon Brendle","submitted_at":"2016-10-27T19:05:13Z","abstract_excerpt":"We consider a one-parameter family of strictly convex hypersurfaces in $\\mathbb{R}^{n+1}$ moving with speed $- K^\\alpha \\nu$, where $\\nu$ denotes the outward-pointing unit normal vector and $\\alpha \\geq \\frac{1}{n+2}$. For $\\alpha > \\frac{1}{n+2}$, we show that the flow converges to a round sphere after rescaling. In the affine invariant case $\\alpha=\\frac{1}{n+2}$, our arguments give an alternative proof of the fact that the flow converges to an ellipsoid after rescaling."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08933","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"}