{"paper":{"title":"Quasi-potentials and regularization of currents, and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Tuyen Trung Truong","submitted_at":"2011-11-01T19:20:33Z","abstract_excerpt":"Let $Y$ be a compact K\\\"ahler manifold. We show that the weak regularization $K_n$ of Dinh and Sibony for the diagonal $\\Delta_Y$ (see Section 2 for more detail) is compatible with wedge product in the following sense:\n  If $T$ is a positive $dd^c$-closed $(p,p)$ current and $\\theta$ is a smooth $(q,q)$ form then there is a sequence of positive $dd^c$-closed $(p+q,p+q)$ currents $S_n$ whose masses converge to 0 so that $-S_n\\leq K_n(T\\wedge \\theta)-K_n(T)\\wedge \\theta \\leq S_n$ for all $n$.\n  We also prove a result concerning the quasi-potentials of positive closed currents. We give two applic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0278","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"}