ARCHIMEDES'PRINCIPLE OF FLOTATION AND FLOATING BODIES:CONSTRUCTION,EXTENSIONS AND RELATED PROBLEMS  

作　　者：Chunyan LIU Elisabeth M.WERNER Deping YE Ning ZHANG 刘春艳;Elisabeth M.WERNER;叶德平;张宁(School of Mathematics and Computer Science,Wuhan Polytechnic University,Wuhan,430048,China;Department of Mathematics,Case Western Reserve University,Cleveland,OH,44106,USA;Department of Mathematics and Statistics,Memorial University of Newfoundland,St.John’s,Newfoundland,Canada,A1C 5S7;School of Mathematics and Statistics,Huazhong University of Science and Technology,1037 Luoyu Road,Wuhan,430074,China)

机构地区：[1]School of Mathematics and Computer Science,Wuhan Polytechnic University,Wuhan,430048,China [2]Department of Mathematics,Case Western Reserve University,Cleveland,OH,44106,USA [3]Department of Mathematics and Statistics,Memorial University of Newfoundland,St.John’s,Newfoundland,Canada,A1C 5S7 [4]Department of Mathematics and Statistics,Memorial University of Newfoundland,St.John’s,School of Mathematics and Statistics,Huazhong University of Science and Technology,1037 Luoyu Road,Wuhan,430074,China

出　　处：《Acta Mathematica Scientia》2025年第1期237-256,共20页数学物理学报(B辑英文版)

基　　金：supported by the Research Funding of Wuhan Polytechnic University(2024RZ083);Elisabeth M.Werner’s work was supported by the NSF grant DMS-2103482.Deping Ye’s work was supported by an NSERC grant,Canada.Ning Zhang’s work was supported by the NSF of China(11901217,11971005).

摘　　要：In this article,we explain how the famous Archimedes’principle of flotation can be used to construct various floating bodies.We survey some of the most important results regarding the floating bodies,including their relations with affine surface area and projection body,their extensions in different settings such as space forms and log-concave functions,and mention some associated open problems.

关 键 词：flfoating body affine surface area log-concave functions 

分 类 号：O17[理学—数学]