{"paper":{"title":"Maximal bottom of spectrum or volume entropy rigidity in Alexandrov geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Jiang Yin","submitted_at":"2017-02-15T03:59:16Z","abstract_excerpt":"In \\cite{LiWang2001complete1,LiWang2001complete2}, Li-Wang proved a splitting theorem for an n-dimensional Riemannian manifold with $Ric\\geqslant -(n-1)$ and the bottom of spectrum $\\lambda_0(M)=\\frac{(n-1)^2}{4}$. For an n-dimensional compact manifold $M$ with $Ric\\geqslant-(n-1)$ with the volume entropy $h(M)=n-1$, Ledrappier-Wang \\cite{LeW2010volent} proved that the universal cover $\\tilde{M}$ is isometric to the hyperbolic space $\\mathbb{H}^n$. We will prove analogue theorems for Alexandrov spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04461","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"}