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Throughout history, many mathematicians have studied and proved numerous geometric inequalities. The first example was the classical isoperimetric inequality in the plane. Later, many variants of this inequality and generalizations to higher dimensions were obtained. Corresponding to them, several relative isoperimetric inequalities appeared. In these inequalities, the area (volume) of a set E was compared with the relative perimeter (the measure of part of the boundary of E, in particular the part of the boundary which is contained in other open set G). The aim of this book is to present a precise study of relative geometric inequalities, in which we compare not only the relative volume and the relative perimeter, but also other relative geometric magnitudes. We shall look for the infimum and the supremum of the considered ratios, and for the sets which attain these bounds (maximizers and minimizers). We shall also obtain relative geometric inequalities for centrally symmetric compact, convex surfaces using the intrinsic distance. Finally, several applications of these inequalities, to other fields of mathematics and to real life problems, are described.
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is an associate professor at the dept. of Innovation and Didactical Education at University of Alicante. She received her P.h.D. degree from University of Alicante in 2005. Her research interests are convex and discrete geometry, and also didactical reserch and education. She has several publications in refereed journals and conferences.
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- PublisherLAP LAMBERT Academic Publishing
- Publication date2010
- ISBN 10 3838394690
- ISBN 13 9783838394695
- BindingPaperback
- Number of pages96
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Book Description Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Throughout history, many mathematicians have studied and proved numerous geometric inequalities. The first example was the classical isoperimetric inequality in the plane. Later, many variants of this inequality and generalizations to higher dimensions were obtained. Corresponding to them, several relative isoperimetric inequalities appeared. In these inequalities, the area (volume) of a set E was compared with the relative perimeter (the measure of part of the boundary of E, in particular the part of the boundary which is contained in other open set G). The aim of this book is to present a precise study of relative geometric inequalities, in which we compare not only the relative volume and the relative perimeter, but also other relative geometric magnitudes. We shall look for the infimum and the supremum of the considered ratios, and for the sets which attain these bounds (maximizers and minimizers). We shall also obtain relative geometric inequalities for centrally symmetric compact, convex surfaces using the intrinsic distance. Finally, several applications of these inequalities, to other fields of mathematics and to real life problems, are described. 96 pp. Englisch. Seller Inventory # 9783838394695
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Book Description Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Throughout history, many mathematicians have studied and proved numerous geometric inequalities. The first example was the classical isoperimetric inequality in the plane. Later, many variants of this inequality and generalizations to higher dimensions were obtained. Corresponding to them, several relative isoperimetric inequalities appeared. In these inequalities, the area (volume) of a set E was compared with the relative perimeter (the measure of part of the boundary of E, in particular the part of the boundary which is contained in other open set G). The aim of this book is to present a precise study of relative geometric inequalities, in which we compare not only the relative volume and the relative perimeter, but also other relative geometric magnitudes. We shall look for the infimum and the supremum of the considered ratios, and for the sets which attain these bounds (maximizers and minimizers). We shall also obtain relative geometric inequalities for centrally symmetric compact, convex surfaces using the intrinsic distance. Finally, several applications of these inequalities, to other fields of mathematics and to real life problems, are described. Seller Inventory # 9783838394695
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Book Description Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Cerdan Sala Anais an associate professor at the dept. of Innovation and Didactical Education at University of Alicante. She received her P.h.D. degree from University of Alicante in 2005. Her research interests are convex and discr. Seller Inventory # 5419693
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