{"paper":{"title":"Inverse scattering at fixed energy on surfaces with Euclidean ends","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Colin Guillarmou (DMA), Leo Tzou, Mikko Salo","submitted_at":"2010-04-02T10:49:40Z","abstract_excerpt":"On a fixed Riemann surface $(M_0,g_0)$ with $N$ Euclidean ends and genus $g$, we show that, under a topological condition, the scattering matrix $S_V(\\la)$ at frequency $\\la > 0$ for the operator $\\Delta+V$ determines the potential $V$ if $V\\in C^{1,\\alpha}(M_0)\\cap e^{-\\gamma d(\\cdot,z_0)^j}L^\\infty(M_0)$ for all $\\gamma>0$ and for some $j\\in\\{1,2\\}$, where $d(z,z_0)$ denotes the distance from $z$ to a fixed point $z_0\\in M_0$. The topological condition is given by $N\\geq\\max(2g+1,2)$ for $j=1$ and by $N\\geq g+1$ if $j=2$. In $\\rr^2$ this implies that the operator $S_V(\\la)$ determines any $C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0315","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"}