{"paper":{"title":"Lipschitz-Killing curvatures and polar images","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.AG","authors_text":"Nicolas Dutertre (I2M)","submitted_at":"2015-12-09T08:08:56Z","abstract_excerpt":"We relate the Lipschitz-Killing measures of a definable set $X \\subset \\mathbb{R}^n$ in an o-minimal structure to the volumes of generic polar images. For smooth submanifolds of $\\mathbb{R}^n$, such results were established by Langevin and Shifrin.Then we give infinitesimal versions of these results. As a corollary, we obtain a relation between the polar invariants of Comte and Merle and the densities of generic polar images."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02780","kind":"arxiv","version":1},"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"}