{"id":{"repo_id":"wichita-thes","oai_identifier":"oai:soar.wichita.edu:10057/30114"},"canonical_url":"https://search.dev.ndltd.org/etd/wichita-thes/oai:soar.wichita.edu:10057/30114","repository":{"repo_id":"wichita-thes","name":"Wichita State University","base_url":"https://soar.wichita.edu/oai/request"},"display":{"title":"On the additive properties of geometric measures","abstract":"We study the Minkowski sums of compact sets in $R^n$, focusing on different geometric measures of these sums. We establish the equality conditions for the fractionally superadditive volume inequalities, resolve the Dyn–Farkhi conjecture in the case n = 2, and compute upper and lower bounds for the Schneider non-convexity index.","abstract_html":"We study the Minkowski sums of compact sets in <span class=\"etd-inline-math\">R<sup>n</sup></span>, focusing on different geometric measures of these sums. We establish the equality conditions for the fractionally superadditive volume inequalities, resolve the Dyn–Farkhi conjecture in the case n = 2, and compute upper and lower bounds for the Schneider non-convexity index.","abstract_has_math":true,"creators":["Meyer, Mark"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-05","date_published":"2025-05","updated_at":"2026-07-24T06:05:48Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/30114"],"render_values":[{"text":"hdl:10057/30114","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2025-05"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/30114"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["We study the Minkowski sums of compact sets in $R^n$, focusing on different geometric measures of these sums. We establish the equality conditions for the fractionally superadditive volume inequalities, resolve the Dyn–Farkhi conjecture in the case n = 2, and compute upper and lower bounds for the Schneider non-convexity index."]},{"key":"dc:title","label":"Title","values":["On the additive properties of geometric measures"]}]}],"canonical_facts":{"dc:date.issued":["2025-05"],"dc:description.other":["We study the Minkowski sums of compact sets in $R^n$, focusing on different geometric measures of these sums. We establish the equality conditions for the fractionally superadditive volume inequalities, resolve the Dyn–Farkhi conjecture in the case n = 2, and compute upper and lower bounds for the Schneider non-convexity index."],"dc:identifier":["hdl:10057/30114"],"dc:title":["On the additive properties of geometric measures"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T06:05:48Z"}