{"paper":{"title":"On common zeros of eigenfunctions of the Laplace operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Boris Kazarnovskii, Dmitri Akhiezer","submitted_at":"2016-05-24T12:01:42Z","abstract_excerpt":"We consider the eigenfunctions of the Laplace operator $\\Delta $ on a compact Riemannian manifold of dimension $n$. For $M$ homogeneous with irreducible isotropy representation and for a fixed eigenvalue of $\\Delta $ we find the average number of common zeros of $n$ eigenfunctions. For this we compute the volume of the image of $M$ under an equivariant immersion into a sphere."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07397","kind":"arxiv","version":3},"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"}