{"paper":{"title":"Plurisuperharmonicity of reciprocal energy function on Teichmuller space and Weil-Petersson metrics","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":"2019-01-15T21:26:02Z","abstract_excerpt":"We consider harmonic maps$u(z): \\mathcal{X}_z\\to N$ in a fixed homotopy class from Riemann surfaces $\\mathcal{X}_z$ of genus $g\\geq 2$ varying in the Teichm\\\"u{}ller space $\\mathcal T$ to a Riemannian manifold $N$ with non-positive Hermitian sectional curvature.\n  The energy function $E(z)=E(u(z))$ can be viewed as a function on $\\mathcal T$ and we study its first and the second variations. We prove that the reciprocal energy function $E(z)^{-1}$ is plurisuperharmonic on Teichm\\\"uller space. We also obtain the (strict) plurisubharmonicity of $\\log E(z)$ and $E(z)$. As an application, we get th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05048","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"}