{"paper":{"title":"Global gauges and global extensions in optimal spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.FA","authors_text":"Mircea Petrache, Tristan Rivi\\`ere","submitted_at":"2013-02-22T17:43:03Z","abstract_excerpt":"We consider the problem of extending functions \\phi:\\to S^n to functions u:B^{n+1}\\to S^n for n=2,3. We assume \\phi to belong to the critical space W^{1,n} and we construct a W^{1,(n+1,\\infty)}-controlled extension u. The Lorentz-Sobolev space W^{1,(n+1,\\infty)} is optimal for such controlled extension. Then we use such results to construct global controlled gauges for L^4-connections over trivial SU(2)-bundles in 4 dimensions. This result is a global version of the local Sobolev control of connections obtained by K. Uhlenbeck."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5659","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"}