{"paper":{"title":"Energy of Twisted Harmonic Maps of Riemann Surfaces","license":"","headline":"","cross_cats":["math.GN"],"primary_cat":"math.DG","authors_text":"Richard A. Wentworth, William M. Goldman","submitted_at":"2005-06-10T21:00:28Z","abstract_excerpt":"The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface $S$ is a function $E_\\rho$ on Teichm\\\"uller space $\\Teich$ which is a qualitative invariant of the holonomy representation $\\rho$ of $\\pi_1(S)$. Adapting ideas of Sacks-Uhlenbeck, Schoen-Yau and Tromba, we show that the energy function $E_\\rho$ is proper for any convex cocompact representation of the fundamental group. More generally, if $\\rho$ is a discrete embedding onto a normal subgroup of a convex cocompact group $\\Gamma$, then $E_\\rho$ defines a proper function on the quotie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506212","kind":"arxiv","version":2},"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"}