{"paper":{"title":"Mass and Extremals Associated with the Hardy-Schr\\\"odinger Operator on Hyperbolic Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hardy Chan, Luiz Fernando de Oliveira Faria, Nassif Ghoussoub, Saikat Mazumdar, Shaya Shakerian","submitted_at":"2017-10-03T16:43:16Z","abstract_excerpt":"We consider the Hardy-Schr\\\"odinger operator $ -\\Delta_{\\mathbb{B}^n}-\\gamma{V_2}$ on the Poincar\\'e ball model of the Hyperbolic space ${\\mathbb{B}^n}$ ($n \\geq 3$). Here $V_2$ is a well chosen radially symmetric potential, which behaves like the Hardy potential around its singularity at $0$, i.e., $V_2(r)\\sim \\frac{1}{r^2}$. Just like in the Euclidean setting, the operator $ -\\Delta_{\\mathbb{B}^n}-\\gamma{V_2}$ is positive definite whenever $\\gamma <\\frac{(n-2)^2}{4}$, in which case we exhibit explicit solutions for the equation $$-\\Delta_{\\mathbb{B}^n}u-\\gamma{V_2}u=V_{2^*(s)}u^{2^*(s)-1}\\qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01271","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"}