{"paper":{"title":"Kato's inequality and form boundedness of Kato potentials on arbitrary Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Batu G\\\"uneysu","submitted_at":"2011-05-03T10:11:56Z","abstract_excerpt":"Let $(M,g)$ be a Riemannian manifold with Laplace-Beltrami operator $-\\Delta$ and let $E\\to M$ be a Hermitian vector bundle with a Hermitian covariant derivative $\\nabla$. Furthermore, let H(0) denote the Friedrichs realization of $\\nabla^*\\nabla$ and let $V$ be a potential. We prove that $V^-$ is H(0)-form bounded with bound $<1$, if the function $\\max\\sigma(V^-)$ is in the Kato class of $(M,g)$. In particular, this gives a sufficient condition under which one can define the form sum $H(V):=H(0)\\dotplus V$ on arbitrary Riemannian manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0532","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"}