On Relative Geometric Inequalities: Comparing relative geometric measures

Ana Cerdan Sala

Published by LAP LAMBERT Academic Publishing, 2010
ISBN 10: 3838394690 / ISBN 13: 9783838394695
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Synopsis: 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.

About the Author: 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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Title: On Relative Geometric Inequalities: ...
Publisher: LAP LAMBERT Academic Publishing
Publication Date: 2010
Binding: Paperback
Book Condition: Good

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Book Description LAP Lambert Acad. Publ. Sep 2010, 2010. Taschenbuch. Condition: Neu. 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 LAP Lambert Acad. Publ. Sep 2010, 2010. Taschenbuch. Condition: Neu. 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 LAP Lambert Acad. Publ. Sep 2010, 2010. Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand 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 LAP Lambert Academic Publishing, Germany, 2010. Paperback. Condition: New. Language: English. Brand new Book. 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 # KNV9783838394695

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