{"paper":{"title":"Mountain pass energies between homotopy classes of maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Daniel Stern","submitted_at":"2018-09-10T14:43:03Z","abstract_excerpt":"For non-homotopic maps $u,v\\in C^{\\infty}(M,N)$ between closed Riemannian manifolds, we consider the smallest energy level $\\gamma_p(u,v)$ for which there exist paths $u_t\\in W^{1,p}(M,N)$ connecting $u_0=u$ to $u_1=v$ with $\\|du_t\\|_{L^p}^p\\leq \\gamma_p(u,v)$. When $u$ and $v$ are $(k-2)$-homotopic, work of Hang and Lin shows that $\\gamma_p(u,v)<\\infty$ for $p\\in [1,k)$, and using their construction, one can obtain an estimate of the form $\\gamma_p(u,v)\\leq \\frac{C(u,v)}{k-p}$. When $M$ and $N$ are oriented, and $u$ and $v$ induce different maps on real cohomology in degree $k-1$, we show tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03361","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"}