{"paper":{"title":"Remarks on the metric induced by the Robin function II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Diganta Borah","submitted_at":"2012-07-02T13:21:48Z","abstract_excerpt":"Let $D$ be a smoothly bounded pseudoconvex domain in $\\mathbf C^n$, $n > 1$. Using the Robin function $\\La(p)$ that arises from the Green function $G(z, p)$ for $D$ with pole at $p \\in D$ associated with the standard sum-of-squares Laplacian, N. Levenberg and H. Yamaguchi had constructed a K\\\"{a}hler metric (the so-called $\\La$-metric) on $D$. Assume that $D$ is strongly pseudoconvex and $ds^2$ denotes the $\\La$-metric on $D$. In this article, first we prove that the holomorphic sectional curvature of $ds^2$ along normal directions converges to a negative constant near the boundary of $D$. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0371","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"}