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Let $g_1$ be a Riemannian metric on $X$ such that $g_1 = g_0$ outside a compact in $X$, and with sectional curvatures $K_{g_1}$ satisfying $K_{g_1} \\leq -1$. The identity map $id : (X, g_0) \\to (X, g_1)$ is bi-Lipschitz, and hence induces a homeomorphism between the boundaries at infinity of $(X, g_0)$ and $(X, g_1)$, which we denote by $\\hat{id}_{g_0, g_1} : \\partial_{g_0} X \\to \\partial_{g_1} X$. We show that if the boundary map $\\"},"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":"1812.04888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-12T10:46:11Z","cross_cats_sorted":[],"title_canon_sha256":"084f649bb0c67bdae27a935d36e2d5e50e2e436e0ee61b7e48672e81fbc968ec","abstract_canon_sha256":"9a97fe454c31f71ecd2374e0348ed6d530e84138ecbbd8314c4d5ea6f1a67c5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:27.037790Z","signature_b64":"nQcoeNmHGbkrDx9tbOnrs1OMJJR7uSin0iPmqUMzB36WNwPyX1cN81T524eODuITE9fiX+SGDXXJmiLdLMKDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b06488f4272e381c2ca89fa4eaf7430f7a6f4e8bcb57b77aae4ccbf247ce4d2","last_reissued_at":"2026-05-17T23:58:27.036971Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:27.036971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moebius rigidity for compact deformations of negatively curved manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kingshook Biswas","submitted_at":"2018-12-12T10:46:11Z","abstract_excerpt":"Let $(X, g_0)$ be a complete, simply connected Riemannian manifold with sectional curvatures $K_{g_0}$ satisfying $-b^2 \\leq K_{g_0} \\leq -1$ for some $b \\geq 1$. Let $g_1$ be a Riemannian metric on $X$ such that $g_1 = g_0$ outside a compact in $X$, and with sectional curvatures $K_{g_1}$ satisfying $K_{g_1} \\leq -1$. The identity map $id : (X, g_0) \\to (X, g_1)$ is bi-Lipschitz, and hence induces a homeomorphism between the boundaries at infinity of $(X, g_0)$ and $(X, g_1)$, which we denote by $\\hat{id}_{g_0, g_1} : \\partial_{g_0} X \\to \\partial_{g_1} X$. 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