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The main objective of the present paper is to study the Hausdorff dimension of the image sets $B^H(F+t)$, $F\\subset\\mathbb{R}^N$ and $t\\in\\mathbb{R}^N$, in the dimension case $d<\\tfrac{1}{H_1}+\\cdots+\\tfrac{1}{H_N}$. Following the seminal work of Kaufman (1989), we establish uniform dimensional properties on $B^H$, answering questions raised by Khoshnevisan et al (2006) and Wu and Xiao (2009).\n  For the purpose of this work, we introduce a refinement of the secto"},"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":"1507.08466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-30T11:55:09Z","cross_cats_sorted":[],"title_canon_sha256":"b1acdca525e5725dd5e9da777768932425f4d5293e5aedd618200908c09e0401","abstract_canon_sha256":"88cbc0206ea30753f90ab428edf7ae614ee2c994da487c283df899019df9a9d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:06.359142Z","signature_b64":"jjoqgEYYX2Jw0p5SHGTcmfsMpVeCEZosw9YKyjHVjA2Y5EXo0LwxcAqa2NAiK4BCxVcRiDW57I0lxftToyB5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5e162e1b7a544ecc05f1ea9699e6ca7d0716395f08527d935bb718ddd59320c","last_reissued_at":"2026-05-18T01:36:06.358697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:06.358697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Image sets of fractional Brownian sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Paul Balan\\c{c}a","submitted_at":"2015-07-30T11:55:09Z","abstract_excerpt":"Let $B^H = \\{ B^H(t), t\\in\\mathbb{R}^N \\}$ be an $(N,d)$-fractional Brownian sheet with Hurst index $H=(H_1,\\dotsc,H_N)\\in (0,1)^N$. 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