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Let $q>n$ and $A>0$ be some real numbers satisfying $|M|^\\frac{1}{n}(1+\\|B\\|_q)\\leq A$. Suppose that $\\phi(M)\\subset B(p_0,R)$, where $p_0$ is a center of gravity of $M$ and radius $R<\\frac{\\pi}{2}$. We prove that there exists a positive constant $\\e$ depending on $q$, $n$, $R$ and $A$ such that if $n(1+\\|H\\|_\\infty^2)-\\e\\leq \\l_1$, then $M$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1508.06975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-27T19:11:22Z","cross_cats_sorted":[],"title_canon_sha256":"814efb644200c3210963bccb3973b480da8eae5e15d1d7391fd95643ae3a4891","abstract_canon_sha256":"6430976c3720e06bc5e5de7f7b4c6a2b6c735815a3c8dce1418f9f8166ce725d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:40.413544Z","signature_b64":"3kqwKmgwp3pqy7wbVzmxyn1h/LAQy2ukU0vli5DkbWZKKYBr/+tmP/DlOHL4RcqatntXgqwqPLIDhl8XoPKrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ad679587fdbb4f49940879e0692b85a6ff75e5413f27e6ec7a1e912bd665f1b","last_reissued_at":"2026-05-18T01:34:40.412813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:40.412813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Eigenvalue Pinching Theorem for Compact Hypersurfaces in A Sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hongwei Xu, Yingxiang Hu","submitted_at":"2015-08-27T19:11:22Z","abstract_excerpt":"In this article, we prove an eigenvalue pinching theorem for the first eigenvalue of the Laplacian on compact hypersurfaces in a sphere. 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