{"paper":{"title":"Plurisubharmonicity and geodesic convexity of energy function on Teichm\\\"uller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Genkai Zhang, Inkang Kim, Xueyuan Wan","submitted_at":"2018-09-01T21:29:05Z","abstract_excerpt":"Let $\\pi:\\mc{X}\\to \\mc{T}$ be Teichm\\\"uller curve over Teichm\\\"uller space $\\mc{T}$, such that the fiber $\\mc{X}_z=\\pi^{-1}(z)$ is exactly the Riemann surface given by the complex structure $z\\in \\mc{T}$. For a fixed Riemannian manifold $M$ and a continuous map $u_0: M\\to \\mc{X}_{z_0}$, let $E(z)$ denote the energy function of the harmonic map $u(z):M\\to \\mc{X}_z$ homotopic to $u_0$, $z\\in \\mathcal T$. We obtain the first and the second variations of the energy function $E(z)$, and show that $\\log E(z)$ is strictly plurisubharmonic on Teichm\\\"uller space, from which we give a new proof on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00255","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"}