{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,24]],"date-time":"2024-08-24T00:13:27Z","timestamp":1724458407645},"reference-count":14,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,23]],"date-time":"2022-07-23T00:00:00Z","timestamp":1658534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020, UIDP\/04106\/2020","UIDB\/04106\/2020, UIDP\/04106\/2020"],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"Consider a point on a convex surface in Rd, d\u22652 and a plane of support \u03a0 to the surface at this point. Draw a plane parallel with \u03a0 cutting a part of the surface. We study the limiting behavior of this part of the surface when the plane approaches the point, being always parallel with \u03a0. More precisely, we study the limiting behavior of the normalized surface area measure in Sd\u22121 induced by this part of the surface. In this paper, we consider two cases: (a) when the point is regular and (b) when it is singular conical, that is the tangent cone at the point does not contain straight lines. In Case (a), the limit is the atom located at the outward normal vector to \u03a0, and in Case (b), the limit is equal to the measure induced by the part of the tangent cone cut off by a plane.<\/jats:p>","DOI":"10.3390\/axioms11080356","type":"journal-article","created":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T02:49:02Z","timestamp":1658717342000},"page":"356","source":"Crossref","is-referenced-by-count":2,"title":["Local Structure of Convex Surfaces near Regular and Conical Points"],"prefix":"10.3390","volume":"11","author":[{"given":"Alexander","family":"Plakhov","sequence":"first","affiliation":[{"name":"Center for R & D in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"},{"name":"Institute for Information Transmission Problems, 127051 Moscow, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Pogorelov, A.V. (1973). 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Optim."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1002\/1522-2616(200106)226:1<153::AID-MANA153>3.0.CO;2-2","article-title":"Newton\u2019s problem of the body of minimal resistance in the class of convex developable functions","volume":"226","author":"Peletier","year":"2001","journal-title":"Math. Nachr."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s00205-008-0137-1","article-title":"Billiards and two-dimensional problems of optimal resistance","volume":"194","author":"Plakhov","year":"2009","journal-title":"Arch. Ration. Mech. Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1070\/SM2005v196n06ABEH000904","article-title":"Newton\u2019s aerodynamic problem in media of chaotically moving particles","volume":"196","author":"Plakhov","year":"2005","journal-title":"Sbornik Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10107-014-0756-2","article-title":"The numerical solution of Newton\u2019s problem of least resistance","volume":"147","author":"Wachsmuth","year":"2014","journal-title":"Math. Program."},{"key":"ref_14","first-page":"217","article-title":"On generalized Newton\u2019s aerodynamic problem","volume":"82","author":"Plakhov","year":"2021","journal-title":"Trans. Mosc. Math. Soc."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/8\/356\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T07:49:23Z","timestamp":1724399363000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/8\/356"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,23]]},"references-count":14,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["axioms11080356"],"URL":"https:\/\/doi.org\/10.3390\/axioms11080356","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,7,23]]}}}