{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T10:50:06Z","timestamp":1753872606905,"version":"3.41.2"},"reference-count":17,"publisher":"AIP Publishing","issue":"12","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2007,12,1]]},"abstract":"<jats:p>We investigate the problem of minimizing the moment of inertia among convex surfaces in R3 having a specified surface area. First, we prove that a minimizing surface exists, and derive a necessary condition holding at points of positive curvature. Then we show that an equilateral triangular prism is the optimal triangular prism, that the cube is the optimal rectangular prism, and that the sphere is (locally) optimal among ellipsoids. Many examples of convex surfaces are examined, among which the lowest moment of inertia is achieved by a truncated tetrahedron. The problem of finding the global minimizing surface remains open. The analogous problem in two dimensions has been solved by Sachs and later by Hall, who showed that the equilateral triangle minimizes the moment of inertia, among all convex curves with given length.<\/jats:p>","DOI":"10.1063\/1.2823888","type":"journal-article","created":{"date-parts":[[2008,1,3]],"date-time":"2008-01-03T18:38:20Z","timestamp":1199385500000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["On convex surfaces with minimal moment of inertia"],"prefix":"10.1063","volume":"48","author":[{"given":"P.","family":"Freitas","sequence":"first","affiliation":[{"name":"University of Lisbon Departamento de Matem\u00e1tica, Faculdade de Motricidade Humana (TU Lisbon) and Group of Mathematical Physics, , Complexo Interdisciplinar, Av. Prof. Gama Pinto 2, P-1649-003 Lisboa, Portugal"}]},{"given":"R. S.","family":"Laugesen","sequence":"additional","affiliation":[{"name":"University of Illinois Department of Mathematics, , Urbana, Illinois 61801, USA"}]},{"given":"G. F.","family":"Liddell","sequence":"additional","affiliation":[{"name":"University of Otago Department of Mathematics, , P.O. Box 56, Dunedin, New Zealand"}]}],"member":"317","published-online":{"date-parts":[[2007,12,28]]},"reference":[{"key":"2023080207455017300_c1","first-page":"19","volume":"502","year":"1998","journal-title":"J. Reine Angew. Math."},{"key":"2023080207455017300_c2","first-page":"121","volume":"8","year":"1958\/59","journal-title":"Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg, Math.-Naturwiss. Reihe"},{"key":"2023080207455017300_c3","first-page":"103","volume":"11","year":"1960","journal-title":"Acta Math. Acad. Sci. Hung."},{"key":"2023080207455017300_c4","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/BF02792548","volume":"45","year":"1985","journal-title":"J. Anal. 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